@SpookDog I've had good results with car shampoo in the past, it has the same lubricating qualities as Fairy Liquid but without all the nasty elements which rot the rims from the inside.
I used to have this problem fairly often with Avon TrailRiders in the recommended sizes on DTR rims; excellent tyres but it was always difficult to get them to pop the bead and sometimes I had to deflate the tyre completely, remove it and refit 90 degrees around the rim. This is even after blowing them up to 50psi with the valve core removed using a compressor. I've had to leave them at this pressure for 30 minutes or so in the past as well, and resort to other tricks like hammering the sidewall kind of downwards with a rubber mallet at the affected spot (watch the rim!). It was only ever a problem with this particular make and model of tyre, they were ace on the road but Avons have always been a bit strange.
Most bike shops fit tyres using the 50psi-no-valve-core-compressor method. This might not be what you want to hear but if your rim responds to this treatment by exploding then it was a pretty safe bet it was sufficiently corroded to be unsafe to use. Slightly off topic but there's a well-known story called "The Imprint of Death" they tell kids at tech colleges about a tyre fitter who was fitting a truck tyre and didn't bother using the circus animal-sized cage they put them in to pop the bead; it went bang and half of him ended up stuck to the ceiling. A bike tyre won't do that but still has a lot of energy stored in it, enough to do someone serious harm if they're stood right next to it. I think if I was worried whether a crusty rim of mine could handle 50psi, I'd be on the lookout for a new wheel to be honest.
