Test final and driver. One of them is almost certainly toast.
When you replace the bad ones, don't just turn it on and try it. May be other damage that can cause the replacements to go up in smoke.
With the mirror board removed, see if you get 12.5v or better at TP9 in SSB. If so, then go to AM and check again in TX w/ no modulation. Should be between 5.4v and 6v. If you are not getting around those values, you will need to go check the regulator and its associated driver (darlington pair). I am guessing that regulator is a resistor after that kind of abuse, so expect issues there.
After the regulator gets the attention it needs, with the mirror board still removed, measure the gate voltage of the replaced mosfet. If you can adjust the gate voltage below 3v, you are good. Turn it down as far as it goes so that when you put the current meter across the test points for the actual bias measurement, they are not immediately turning on hard.
Don't lose the insulators under those mosfets, and don't lose the little ceramic insulators for its mounting screw, they are very necessary. Continuity between the mosfet mounting tab and the heat sync will present the same symptoms, dead short, since the tab is connected to the drain internally.
I hope you have some heat sync compound on hand, you are going to need it.