Every sort of true 600 ohm mixing system I've seen starts with a set of amps that can drive 600 ohms, has 600 ohm in/out amps for summing gain, master fade, then another set of 600 ohm amps for output. Many broadcast consoles have a few input channels using 600 ohm repeat coils, which will still require an external source capable of appropriate drive. The Altec 250SU and 250T3 consoles used the 15K:600 15095 octal transformers for bridging inputs, but you get about -14 dB loss that way.
If you want to stay passive up to the makeup amps, you probably need bridging input transformers of some sort. Otherwise, consider various buffer amp inputs that can present higher input Z and likewise drive the mixing stage.
My long term restoration pile ha a number of vintage 600 ohm mixers on it, one being a large custom Altec that used the 9470A amps at input, channel output, and master output. I don't expect to ever use the input stages with mics, so I don't need 45 dB input gain. I will likely add some sort of unity gain buffer amp to the inputs, as the channels themselves already have considerable loss, and there are a lot of them. The thought of 28 channels of bridging transformers hurts, as does the additional losses.