[Gatofeo]

The .380 is NOT too large for the .36 chamber. It will do just fine.
The .375 inch balls are marginal, often offering little more than a slip fit in the chambers of some revolvers. Years ago, I began using .380 inch balls to simplify my stock and stopped buying .375 balls.
The .380 ball, when rammed into the chamber, creates a wider bearing band than the .375 inch ball. This keeps the ball from moving in the chamber from the recoil of firing the other chambers.
It may also aid accuracy, once again that wider bearing band offering a greater surface area for the rifling to grip.
In any case, the .380 ball does no harm.
As for being harder to seat in the chamber, the difference is negligible. Yeah, you can tell the difference but it doesn't put any appreciably greater strain on the rammer than using a .375 inch ball.
Yes, it does cut a full ring of lead that tends to cling to the rammer but this is a minor inconvenience to ensure that the ball stays put in the chamber and offers greater obturation (sealing) in the bore.
It takes a second to flick off the offending ring of lead with your fingernail or a small screwdriver. If you care to bother with it at all.
For some revolvers, .375 inch works fine. But for others, it's simply too small. My Colt 2nd generation 1851 Navy has chambers of .373 to .374 inch. For it, I use the .380 ball. My other .36s use the .380 with equal aplomb, though some might get by with the .375 inch.
Were I you, I'd stick with the .380 balls if you can. Nothing is harmed by doing so, and there are real benefits to using a slightly larger ball.