Look, there's no easy way to do this. I'm working on a project that is inherently multithreaded. Events come in from the operating system and I have to process them concurrently.
The simplest way to deal with testing complex, multithreaded application code is this: If it's too complex to test, you're doing it wrong. If you have a single instance that has multiple threads acting upon it, and you can't test situations where these threads step all over each other, then your design needs to be redone. It's both as simple and as complex as this.
There are many ways to program for multithreading that avoids threads running through instances at the same time. The simplest is to make all your objects immutable. Of course, that's not usually possible. So you have to identify those places in your design where threads interact with the same instance and reduce the number of those places. By doing this, you isolate a few classes where multithreading actually occurs, reducing the overall complexity of testing your system.
But you have to realize that even by doing this, you still can't test every situation where two threads step on each other. To do that, you'd have to run two threads concurrently in the same test, then control exactly what lines they are executing at any given moment. The best you can do is simulate this situation. But this might require you to code specifically for testing, and that's at best a half step towards a true solution.
Probably the best way to test code for threading issues is through static analysis of the code. If your threaded code doesn't follow a finite set of thread safe patterns, then you might have a problem. I believe Code Analysis in VS does contain some knowledge of threading, but probably not much.
Look, as things stand currently (and probably will stand for a good time to come), the best way to test multithreaded apps is to reduce the complexity of threaded code as much as possible. Minimize areas where threads interact, test as best as possible, and use code analysis to identify danger areas.
There are two ways in which abstract base classes are used.
You are specializing your abstract object, but all clients will use the derived class through its base interface.
You are using an abstract base class to factor out duplication within objects in your design, and clients use the concrete implementations through their own interfaces.!
Solution For 1 - Strategy Pattern

If you have the first situation, then you actually have an interface defined by the virtual methods in the abstract class that your derived classes are implementing.
You should consider making this a real interface, changing your abstract class to be concrete, and take an instance of this interface in its constructor. Your derived classes then become implementations of this new interface.

This means you can now test your previously abstract class using a mock instance of the new interface, and each new implementation through the now public interface. Everything is simple and testable.
Solution For 2
If you have the second situation, then your abstract class is working as a helper class.

Take a look at the functionality it contains. See if any of it can be pushed onto the objects that are being manipulated to minimize this duplication. If you still have anything left, look at making it a helper class that your concrete implementation take in their constructor and remove their base class.

This again leads to concrete classes that are simple and easily testable.
As a Rule
Favor complex network of simple objects over a simple network of complex objects.
The key to extensible testable code is small building blocks and independent wiring.
Updated : How to handle mixtures of both?
It is possible to have a base class performing both of these roles... ie: it has a public interface, and has protected helper methods. If this is the case, then you can factor out the helper methods into one class (scenario2) and convert the inheritance tree into a strategy pattern.
If you find you have some methods your base class implements directly and other are virtual, then you can still convert the inheritance tree into a strategy pattern, but I would also take it as a good indicator that the responsibilities are not correctly aligned, and may need refactoring.
Update 2 : Abstract Classes as a stepping stone (2014/06/12)
I had a situation the other day where I used abstract, so I'd like to explore why.
We have a standard format for our configuration files. This particular tool has 3 configuration files all in that format. I wanted a strongly typed class for each setting file so, through dependency injection, a class could ask for the settings it cared about.
I implemented this by having an abstract base class that knows how to parse the settings files formats and derived classes that exposed those same methods, but encapsulated the location of the settings file.
I could have written a "SettingsFileParser" that the 3 classes wrapped, and then delegated through to the base class to expose the data access methods. I chose not to do this yet as it would lead to 3 derived classes with more delegation code in them than anything else.
However... as this code evolves and the consumers of each of these settings classes become clearer. Each settings users will ask for some settings and transform them in some way (as settings are text they may wrap them in objects of convert them to numbers etc.). As this happens I will start to extract this logic into data manipulation methods and push them back onto the strongly typed settings classes. This will lead to a higher level interface for each set of settings, that is eventually no longer aware it's dealing with 'settings'.
At this point the strongly typed settings classes will no longer need the "getter" methods that expose the underlying 'settings' implementation.
At that point I would no longer want their public interface to include the settings accessor methods; so I will change this class to encapsulate a settings parser class instead of derive from it.
The Abstract class is therefore: a way for me to avoid delegation code at the moment, and a marker in the code to remind me to change the design later. I may never get to it, so it may live a good while... only the code can tell.
I find this to be true with any rule... like "no static methods" or "no private methods". They indicate a smell in the code... and that's good. It keeps you looking for the abstraction that you have missed... and lets you carry on providing value to your customer in the mean time.
I imagine rules like this one defining a landscape, where maintainable code lives in the valleys. As you add new behaviour, it's like rain landing on your code. Initially you put it wherever it lands.. then you refactor to allow the forces of good design to push the behaviour around until it all ends up in the valleys.
Best Solution
I think setting up a testdb is a good idea if you're doing automated integration tests or acceptance tests. This usually calls for tests where you test the whole stack (UI, application, database, services etc.) at once.
Unit testing is quite different, they are used during development and not during testing, therefore they should be quicker to run, quicker to change and quicker to write. Its usually a good idea to have unit tests only depend on the small piece of code they're testing. This makes them less brittle, easier to understand and makes developers more willing to run them often.
Using stubs in unit tests is a good idea. The problem you seem to run in to is that if you want to reuse stubs for many tests their behaviour can get very complex, in the worst case you're rebuilding the thing they are supposed to stand in for. This can also happen if you are testing too much at one time.
The solution to this is to have more smaller stubs that only implement the behaviour for one or a few tests and have your tests only test a single behaviour. Tests that test lots of behaviour at once are useful too but they're not unit tests, you should move them to your integration test suite (and can run on a real database). I'm not sure about matlab but in many languages you have mocking frameworks you can use to handle creating stubs and setting up behaviour for you.