The Stax ELS F-81 is one of the most difficult loads one can find. From 40Hz-800Hz the impedance is well above 100 ohms. Around 180Hz the impedance peaks around 512 ohms! Amazing.
Solid state does not like this sort of load. A Zoebel network is highly recommended if using solid state. OTL tube amps are ideal but can be pricey. Transformer coupled tube amps will handle this kind of load.
Power output will depend on required SPL in the listening room. A smallish room with a nearfield set-up will yield SPL in the 90-92 range with a mere 60 watts. I use an ARC D-70, 65 watts, with good results except for clipping if I want to drive things. Or I have an ARC Ref300, 280 watts, that will drive them louder than I like without clipping issues. Well I can clip the Ref300 but then I am pushing the speaker close to failure, probably the transformer.
Any power amp will need to have a large, robust and stable power supply. An ARC VT130, 110 watts, would be ideal with these speakers and is within your budget. The AtmaSphere M-60 would be a great match if maybe just a little under powered.
No matter what you decide in terms of power amps there are a couple of key items that need to be checked in the speaker to keep them healthy.
Check the input RC network resistors. They will have failed. A failed RC network resistor and a large output amp will cause the diaphragm to hit the plates and cause damage. Replace the failed resistors with a good quality wirewound rated for at least 10 watts.
Replace the input fuse. It is worthless. Actually worse than worthless since one assumes they have some protection with the fuse in place. You don't. The stock 2 amp slow-blow will never fail and you will loose a transformer in the process. Replace the fuse with a standard 2 amp normal blow.
Good luck. You have a rare masterpiece. One of the finest speakers I have ever heard. Above 500Hz nearly perfect. Everyone that has heard them, no matter their exposure to high-end, has been floored.