RPM and stock 360 pan

You didn't say that you had done any oiling mods to your oiling system. I lost two factory stock 340s ,shifting in the low 6000s. On both of them, they spun a rod bearing on the driver's side. One was the front and I don't recall which on the other. Just saying.

A MILD 360 might be talking a 268/276/114 cam like the factory one. That cam peaks at around 4800, with a broad plateau. With an automatic, I could see a 5500 rpm 1-2 shift, cuz that puts you into second at 3250. But the 2-3 shift could be much earlier, say 5200 to drop into third at 3600. The trick is to outshift at about the same horsepower, as it inshifts in the next gear.

With a 4 speed, the splits area all the same, and they are tighter, so there's no sense in reving it into the 6000s, unless, like me, you just crave to hear the pipes screaming,lol. For the same 268* cam, you might find a 5200 shift adequate, when it inshifts the next gear at 3750. With good heads, you might be able to stretch it to 5400, and inshift at 3900..... but I think that might be really pushing it.

There is a sticky for the oiling mods.