Sounds like a good excuse to start looking at the dusty dirty old bargain bin stuff at your LGS.
I just talked myself into exactly what you are looking for, except in my case it's an M1917 that's been mildly sporterized, stock cut and reshaped, bolt handle reprofiled, with a lyman receiver sight added.
I couldn't turn it down. It was a shootable rifle with a vintage peep sight for the cost of a tank of diesel.
I have a 38 gallon tank but still..for a functional rifle,
Thats cheap fun