Don't worry about implying lack of ability on my part, assuming I'm a numpty would be a safe starting point! As with most of my bike know-how it was learned when I was sub-10 years old and I can't remember where from!
After patching the inner I put a little bit of air in it and put it back in the tyres, then run my finger around it making sure none of it is pinched. I then put the tyre rim back in, quarter inflate the tube and then 'bounce' the wheel around a couple of times to try and make sure nothing is pinched. I then fully inflate the tyre.
I imagine it doesn't matter too much, but I have old 27" wheels and am using 700c inner-tubes.
Sounds reasonable. I don't think the tyre/tube size thing is an issue. What I do, before inflating, is have the wheel upright and look down onto it. Working round from the valve squeeze one tyre wall in, so I can see the rim tape and make sure the tube isn't sticking out from under. When I get back to the valve, flip the wheel round and check the other side. If the tube is trapped, jibble it until it's in the right place.
Ooh, a thought occurs. Being that your rims are, shall we say, rather venerable, are they the hooked design? Most/all modern rims are and do a much better job of keeping the tyre on.