update / (bump)
I think it is in fact OVER-CURRENT that is killing my MOSFETs.
But, peculiarly, the heatsinks don't get very hot (evidenced by me feeling them immediately after failure). Usually they are just very warm, one being a bit warmer than the other (although I don't remember if it is the low-side or high-side). Probably around 50 to 60*C since I can keep my hand on them for several seconds or indefinably.
Can MOSFETs fail from over current even if they're kept cold? (from perhaps some quantum process I am not familiar with), or does current simply cause the junction to heat up to the point where the FET fails short circuit; i.e. is there a hard limit on how much current a FET can carry even if it is cryogenically cooled?
The die will always be warmer than the casing when power is being dissipated, due to the thermal resistance between them. So it's possible to overheat the die with a reasonably cold casing, in case of excessive dissipation. Additionally, any extra thermal resistance between the casing and the heatsink will make the situation worse. Due to the small thermal mass of the transistor itself, it's possible to overheat the device and then have it cool down again before you can check the temperature, so make sure you measure the case temperature while it's processing full power, ideally with a thermal camera or an IR temperature probe.
While the HY1920P is rated for 90A, similar spec'd FETs from more reputable manufactures claim 60A as the maximum (ones with similar on-state resistance and Ciss).
Ignore the current rating in the datasheet, this is practically useless for real world use. Extreme cooling measures are used to get this figure (I've heard of full immersion in nucleated boiling Freon), and it also assumes all the dissipation comes from conduction losses. Likewise, the 375 W dissipation rating in the datasheet for this TO-220 device is practically unrealizable, even a tenth of this dissipation requires some care.
I've only seen 90A peaks (peak during the peak of the RF envelope shortly after interupter enables the FET driver) on the current transformer a few times when monitoring w/ a scope when running the coil in interrupted mode. When run continuous wave it seems once the RF envelope is stable, the primary resonating current is around 60A peak, or 43A rms.
This sounds like too much current for the performance you're getting. Having a resonant primary in this configuration complicates things by requiring correct tuning between the primary and secondary resonant frequencies, while the secondary resonant frequency changes with spark loading. I've had good success with an untuned primary coil in CW SSTCs. As long as you keep the primary-secondary coupling high (above 0.3 or so), you can push plenty of power without excessive primary magnetizing current.
Also, do you have any current limiting or overcurrent protection? Running a double-resonant CW Tesla Coil with arcs to ground can lead to very high primary currents
Each FET only conducts one half cycle of current, so the RMS per fet should be half. With 20mOhms of on-state resistance each FET should only be generating 9W of heat. This sounds very reasonable, although the peak power dissipation is much higher, 162W.
The full current half of the time equals 71 % (1/sqrt(2)) of the RMS current, while the average current is 50 %. The Rdson is 24 mohm max at room temperature, but 3x this value at Tj = 150 C. This gives 66 W of conduction losses per device, and switching losses come in addition to this. For a TO220 mounted with a screw through the hole, thermal resistance between the casing and heatsink is usually around 1 k/W, in addition to the 0.4 k/W of thermal resistance from the die to the casing. This gives a total thermal gradient of 66 W * 1.4 k/W = 92 k, on top of the 50 - 60 C heatsink temperature. This gives 150 celcius for the junction, without considering switching losses and budgeting for variations in device-heatsink contact. It's plausible that your problems simply come from overheating of the silicon dice inside your MOSFETs. If you want to push over 40 A RMS at 170 V, I would recommend going for more devices in parallel or a bigger package like a TO-247.
What is the best thermal interface material to use for joining the FETs to a heat-sink? Ideally I'd buy some beryllium oxide ceramic insulators, but those are hard to come by, although Digikey does sell them for TO-3 packages. I'm probably going to buy a couple before they become obsolete, even at $20 / piece! aluminum nitride is another pretty decent ceramic insulator but it also is hard to find.
AlN is similar in performance to BeO, and it doesn't have any of the issues with toxicity that BeO does. It's also much cheaper than BeO if you buy it from China on eBay or Aliexpress. 50 cents for TO-220 sized pads, and about twice that for TO-247 sized pads is typical.
Aluminum oxide is the 3rd option but it's thermal conductivity much less. 
! As of now I've been using some sil-pads I have in my junk drawers, of unknown origin (most of them salvaged). For now I might just try modifying my PCB so the heatsinks are electrically tied to the middle pin to eliminiate the need for an insulator, that should provide the best thermal performance, and monitor the heatsinks with my thermal camera to see if I can rule out thermals being the problem.
Aluminium oxide is about an order of magnitude worse than the Nitride, but it's still pretty decent, and also cheaper by at least as much. A 0.63 mm thick pad of Alumina will add around 0.3 k/w for a TO-220 device, which is often much less than the required thermal grease adds. Other factors can easily dominate the thermal resistance here, so to fully benefit from AlN you also need precision flattened and polished heatsink surfaces, a good thermal grease and plenty of clamping force applied evenly across the device package. If you just bolt the device to a stock extruded heatsink with a screw through the hole in the package, I doubt the difference between Al2O3 and AlN would even be visible.
Sil-pads are pretty miserable. Bergquist 900S in 0.23 mm thickness adds over 3 k/w for a TO-220. In my calculation of the junction temperature above, you can add another 120 degrees in this case.
Nothing beats direct contact between the device and the metallic heatsink, when that's possible. But to get the full benefit of this, the heatsink flatness, finish and clamping force matters a lot here too. A well clamped transistor with a thin alumina pad can easily be much better than one without any insulation at all, but mounted using a single screw through the package hole.
* NOTE the RF current was measured by using a DIY current transformer; 30:1 turns ratio around a random green ferrite and a 5 ohm resistor, with voltage amplitude as high as 15V observed, but generally around 5 to 10 volts when run continuous duty
This is an excellent method to measure HF AC currents, I've made many HF CTs like this, and in many applications they perform just as well as 500 dollar Pearson wideband CTs.
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