General tyre question

I've tried searching for an answer for the following online unsuccessfully - maybe I'm searching for the wrong text. I thought it about time I sign up to a forum for Priusses having had ours for 15 months so first post...

This is possibly not specifically a Prius question but I wondered if other owners had come across the same issue. We've booked to have the tyres changed on ours (2016 Prius Mk4 with standard 15" wheels). Both the driveway fitter and tyre centre we've tried have encountered the same problem - when initially put onto the wheel the beads are so far in from where they're supposed to be seated on the rim that they can't inflate the tyre. The driveway fitter suggested we take it into the fitting centre as they have different inflation tools but the centre struggled too. They've suggested the problem may be because the tyres are cold and have been stacked up on their side - they've set them aside in a warm room with some blocks to 'spread' the beads out from each other.

Even if this works we're a bit alarmed - if it's this big a struggle getting the tyres to properly seat on the rims, I feel they're more likely to come unseated in use? I just wondered if anyone else has encountered the same problem?

nb., the tyres we're fitting are Michelin Crossclimate 2s. We'd had these fitted to our last car, a 2008 Civic, which always felt very assured on the road. The Prius feels wayward by comparison and although the lighter steering and skinnier wheels with taller profile tyres are probably a factor (the Civic had 225/45/17s) we can at least change the tyres for ones a bit better suited to variable UK road conditions and weather. These aren't the first tyres we're fitting to our Prius either - the rears are pretty new Goodyear EfficientGrips on account of a puncture that couldn't be fixed and we're only considering replacing them as we're not sure it's wise to mix summer and all weather tyres. The Goodyears went on the rims without issue, although that was warmer weather. The fronts are much older Bridgestones that will be due replacement before too long anyway - they seem to lose traction easily.

We did actually consider whether to swap the 15" wheels for a set of 17" with the tyre size of the higher spec Priuses - presumably as they're a touch wider they're a bit grippier but I don't know if it's particularly noticeable? Given the cost of new wheels, messing around with the tyre pressure monitor, the uplift on the cost of the tyres and likely dent to the car's economy (the Priuses with bigger wheels seem to be less efficient?) we decided not to bother but I'd be interested to know if anyone's any experience comparing the cars with the two different wheel sizes?

Thanks!