If your Mavic is a 15 you are right at the maximum with a 32 tyre but it is not size that is causing the problem with fitting. There are a number of websites covering wheel and tyre sizes but I tend to use that collated by Sheldon Brown (RIP), and also refer to many of his other information pages - particularly wrt Shimano gears.
This probably will not help, but I experienced the same sort of difficulty you are describing fitting Bontrager Hardcase tyres (which I use on my racer); however, with careful positioning and perhaps some guiding by levers they can be put on. On the odd rare occasion I managed it without levers but nearly dislocated my thumbs in the process! I believe the clue is in the name, when they say hardcase it includes the fact that the sidewall is much stiffer and the band also then becomes less flexible.
Objectively, once you have them on, hopefully the puncture resistance will preclude constant removal and refitting.