If you have any spare output transformers, you could test them with the procedure outlined on the link below. It's a bit involved but no worse than doing your income tax. You have one known value already: the output tube is a 6K6 and that requires 8000 ohms primary load impedance, per the chart towards the end of the attached. We don't know the speaker voice coil impedance but it's probably between 4 and 8 ohms. An approximation would have you measure the VC
resistance (disconnect one wire from the transformer so the latter's resistance doesn't enter into the reading) and then multiply by 1.25 for the
impedance. Recall that resistance and impedance are both measured in ohms but represent different characteristics: impedance is "sort of" AC resistance.
Once you get through all that, and make the tests on any output transformers you have, you might have one that works. Or at least you know what turns ratio you need to order. One other note: read the note about audio feedback on the schematic: it tells how to hook up the transformer to avoid feedback.
www.radioremembered.org/outimp.htm