The Gate drive resistors, whether 10 or 22 ohms won't make that much difference. They can have a minor effect on the switching waveform, but not totally stopping operation or causing horrible operation under load. So you don't have to worry about them.
I would focus mainly on your 12V coming into the SMPS and making sure it is not dropping below about 9V or so under load. That will severely compromise operation. In fact, you might want to consider a small 12V Gel SLA battery to use for testing. It can be something anywhere from 6AH (like one used in a UPS) up to a small car battery. Put the battery in parallel with your 12V power supply so your supply charges it most of the time, but for testing, the battery will dump out lots of current so you can run your tests without worry of going into current limiting.
Once you are sure you have a good, solid 12VDC coming into your SMPS, use your scope to watch the Drain switching waveforms. They should be 24V P-P, square wave, with the pulse-width increasing as the load increases. What to watch for: 1) The bottom of the trace near 0V is showing your Vds saturation (the FET's saturation from Drain to Source). If this voltage starts coming up to 0.5, 1, or 2 V, then your FETs are not fully saturated and not switching correctly. They are not being driven fully (12V on the Gates), or they are bad, or they can't handle the switching current. 2) The top of the trace is around 24VDC (2X 12Vin). If this starts to drop to 22, 20, 18V, etc., it means your supply voltage is not adequate. If the top is 18V and not 24V, it means only 9V is getting to the transformer primary. Either the 12V supply is not adequate, the fuse is opening up, the input inductor is bad, etc. PLUS, all the things I just listed will make your FET heatsink get hot!
The snubber circuits getting hot just indicates a lot of noise, spikes, and crap ringing causing the cap to have a low impedance and the resistor to get hot. All of the stuff above can do this too.
The next thing, and this is the scariest part, is that your transformer could be bad/wrong/damaged. If the core is the wrong material, all those things can happen. If there is a shorted winding, same thing. If the core is cracked, the same can happen. If the SMPS is at the wrong switching frequency, it can all happen. All of this would sure suck, but is a possibility. You can swap transformers (I think you said you made a second one) and see if anything changes. Also check the core material, look at the construction, and look for shorts.
So, check your 12V supply - make sure it is staying at a clean 12VDC and can deliver lots of current. Check the FET Drain wavefroms. Check the transformer core and construction.