That's OK, got a ancient Win72a (stock cut down for 12yo) that shoots OK.
Centerfire w/o scope is limited for me too.
A 209/50 Encore OK, caps fire in the center, ten in ten? (just kidding). Otherwise its a mini14 beyond it's range or another 30/30 win94.
Fun anyway, looking forward to it.
Hmmm... I have an equally elderly Winchester 69a that I was thinking about using. Mine is the detachable magazine model, where yours is the tube feed, IIRC. Yes, they do shoot nicely. You could check with Gunpartscorp.com; they might have one of the Model 69 (or 75) target-model stocks. It could be whittled down to a nice sporter stock.
I might also dust off my old Win320. It's a real oddball - an Aussie-built rimfire that Winchester sold in the '70s. Turns out the guy who designed it is the same guy who later started the original Kimber of Oregon. My "Proto-Kimber" shares some parts with the original Kimber 82. Guess I'll see which one like the 100-yd. target better. As for centerfire, I'm still pondering which to use.