I'm rather more concerned with heat sinking a D2PAK. What's that board made of? Is there solid copper inside it?
Nope, the plan was to mount the heatsink on top of the PCB, so that the heat is transferred through the plastic chassis. Unfortunately I did the math wrong before designing that board, and that package has too much thermal resistance.
However mounting TO-3Ps directly to the heatsink seems like it may work.
The better solution is to use resistors, which are smaller and cheaper than heatsinks for the same wattage.
You'd think so, but the exact opposite is true. MOSFETs rated for 200W can be found for about $1, but chassis mount resistors rated to 80W cost around $5.
aluminium pot https://www.amazon.com/dp/B001PZBEKE/ref=twister_B002KMJ8GI?_encoding=UTF8&psc=1
I've definitely considered a bucket full of oil

I guess that's my fallback. If I can get continuous power dissipation, that'd be great, but otherwise a big bucket full of oil would be fine for (I did the math!) about 45 minutes.
Realize that at hundreds of watts even case to sink resistance can become significant.
Absolutely. That design that I have in the OP was made before I realized that case-to-sink resistance existed. It marginally would work with 0°C/W case-to-sink, but fails completely with the actual ~.5°C/W.
You may consider GPU coolers too, some are designed to dissipate 200~300W or more.
This is what really bugs me about cooler manufactures: they do a crap job of actually providing specs for their products. They'll sometimes publish a power rating--meaningless, since they never publish the max temperature. However, they also *never* publish any kind of thermal resistance numbers.
1.) use a FETs which are qualified for linear operation
I'm going to pick this one

. Both the mosfets which I listed are qualified for linear operation, my problem is efficiently removing the heat.
3.) use a lot of FETs at low temperature (separate gate drive and feedback)
That gives me an idea... take a look at the attachment. 0.166°C∕W for the whole thing--but unfortunately I'd be a bit over-budget with 375x KIA Semicon KNH9120A costing $232.