Don't think what you want to do is possible.
Sure, a
PTO generator could drive an electric motor but that would end up costing more than hydraulics.
Forget any kind of flex drive due to power required.
OK, I could see a long
PTO shaft doing the job but that would be cumbersome and prone to trouble.(and very dangereous) as the tractor would need to be a fair distance from the sawmill in order for the shaft to slide in and out to reach both ends of the mill.
With a long shaft unsupported in middle it would probably whip about and kill the operator.
Also the carriage would probably fall off the tracks as it relies on the engine weight to keep it 'on track'.
Your best bet is still a gas engine.
Locally sawmills are offered fo about $4000.CDN with 12 hp engine.
While considered underpowered they still do cut wood.
Why not consider a chainsaw mill? basically a saw clamped to a channel that follows a 2 x 4 as a guide.