I have previously ruled out the Apex PA314 as not having the power desired for this project. It turns out that they have even more crazy solutions, including the PA03 (among others). https://www.apexanalog.com/products/pa03.html

Look at the Package on this thing

It dissipates 500W thermal, and can supply  ±75V at 30A Pk. This is designed for, among other things, driving sonar. The only downside here is price tag, clocking in at nearly $600 dollars on Digikey.

it can be had cheaper on eBay, and they do make some more "down market" offerings that should also work. 

Part of me wants to just shell out ~$150 for one of these premo solutions and be done with this. Buys power, voltage, low harmonic distortion, etc...

On the other hand there's replicating some of the work that's been done by others in the hobbyist community with half bridge FET solutions. The main downside to these is the high harmonic content (I.E. square wave generation), which makes tuning more difficult.