Audio amplifier for 600 ohm headphones
A transformer to make 600 ohm headphones appear as an 8-ohm load for the amplifier may be a bad idea...

Low-impedance headphones are ubiquitous. Plugging one into your transformer would present a load of very low impedance to the amplifier, which might dangerously overheat.

Most audio power amplifiers are designed for an 8-ohm load - some for 4 ohm, and a few for 2 ohm. Any of these won't complain if they see a load of 600 ohms. It is difficult to say if you'll get enough volume from your 'phones before distortion sets in.  Those 600 ohm 'phones might just give you adequate volume when driven directly - no transformer.
It comes down to Ampere-turns. Drive an 8-ohm speaker with the same voltage as 600 ohm headphones. The 8-ohm speaker gets more current through few turns. Headphones get much less current through many more turns. I have 4000 ohm headphones that sound about as loud as 8-ohm headphones when plugged into an amplifier designed for 8 ohms.
So just try any of the amplifiers that are designed for 8 ohm load.