I know people who use .357 and .355 bullets interchangeably without encountering problems. I don't and wouldn't for the simple reason I'm particular about both my guns and ammunition, but I'm the odd one out when it comes to that sort of thing.
It's conceivable using .357 bullets in a .355 barrel could lead to excess pressure, but that's if and only if the .355 barrel is tight. Have you slugged the barrel? Have you accurately measured the bullets?
Didn't think so. If you haven't, and if you're not trying to achieve maximum accuracy, close enough is most probably close enough. If the barrel won't accept lead bullets, it's probably considerably out of standard specification in the oft-cited "first place," so it's not likely to make any difference what you send down it. By the bye, if the barrel has lead fouling problems, it's probably also got copper fouling problems. Those probably don't matter much, but it's been my experience fouling is fouling is fouling.