MAX V does not support SignalTap-II -> how to test the internal logic?

Do it the way we did it in the olden days. Define some pins (as many as you need) as signal access points, and bring interesting signals out to those pins, and connect up an external hardware logic analyzer to the pins. This basically does what SignalTap does, which is just a more flexible version. To change the sampled nodes you will need to recompile and reload. It's a little more time consuming, but in the end it can be just as capable as SignalTap is, depending on how much effort you need to put into your custom logic analyzer implementation.