A circuit diagram of your setup, particularly including your MOSFET driver would be really nice. However, I'll go out on a limb here and suggest that you need to look closely at your drive circuits. It is entirely possible that you are driving your MOSFET gates from 3.3 volt logic. This is perfectly doable - as long as you are using MOSFETs with logic-level gate thresholds. A lot of power MOSFETs need a minimum of 4 volts on the gate to ensure full turn-on. If you're only giving it 3.3 volts, it will only turn on partially, and will dissipate too much power. It's important that you realize that operating a transistor within both voltage and current limits can still kill it if you don't get rid of the heat dissipated, and at high currents it's easy to generate too much heat.
There is a quick check for this (if you want physical proof): Get ready to sacrifice one more MOSFET, but hey, who's counting, right? Drive a heating element full on. Quick like a bunny, measure the voltage across the nichrome and the voltage across the MOSFET. If your MOSFET voltage is not less than about 10% of the nichrome voltage, you're doing something wrong, and less is better in this case. You don't mention your drive voltage, but it has to be less than 25 volts. Let's say it's 20 volts, and let's say the current is 10 amps - this is just to illustrate, OK? Then total power dissipated is 200 watts, and the effective resistance of the total load is 2 ohms. If your MOSFET is fully on, I'd expect an Rds of .1 ohms or less (and this will give a MOSFET voltage about 5% of the nichrome voltage). This would provide a MOSFET dissipation of 10 watts. Without a heat sink, this would kill the MOSFET, so you need a heat sink in any case. And this better not be one of those little U-shaped jobbers, either. You need real heat sink, possibly with a fan. With more airflow you can use a smaller heat sink.
You need to consult the data sheet for your MOSFET to determine both Vgs(th),the threshold gate voltage, and Rds(on), the on-resistance when the gate is properly driven. Then you will need the specs on your heat sink, specifically the thermal resistance to ambient. You will also need to do a little research on how to specify a heat sink.
As for some of your other questions, consider the two voltages you measured. If they both add up to the nominal voltage of your drive converter, you are not drawing too much current, and you don't have a short. You are just fatally abusing your MOSFETs.
It's odd what you say about the bootstrap circuit not performing well above D=0.5. I'm using the same driver chip for a hefty 200 watt power supply where the duty range is quite wide and I've never seen this happening.
I'm switching at 100 kHz - maybe you are using a switch frequency that is too low? Too low a frequency will cause bootstrap power to be a problem.
Another alternative is to use something like a little 2 watt Traco-Power or XP or Murata mini-power module to generate a floating 12 volt for your top FET.
Best Answer
Heat is not the problem. According to other things I've been told on this site, MOSFETs suffer a thermal runaway problem (hot spots on the silicon) when they are used as voltage controlled resistors.
Is it okay to use a MOSFET in its resistive region with a heat sink?
If you use a linear regulator which is made for the purpose, you will avoid the hotspot problem, but will still need a heat sink. However, in my cursory search, I couldn't find anything that could handle 50 V in and which would provide 500 mA output. The LM317 or LM217 might be able to handle it.
If you have your heart set on making a transistor controlled circuit using feedback, you can use a BJT (Darlington?) instead of MOSFET, however I am hesitant to give more specific advice since I'm a little out of the electronics game these days. You will need a heat sink for sure.