I had some Michelin tyres once that were virtually impossible to mount – made worse by the Trek rims, which were tight also!
Normally you stand a pretty good chance at getting them back on without using tyre levers at all. Getting the tyre bead very well into the middle of the rim helps a lot, as does sort of dragging the tyre around in both directions towards your last bit (pulling it tight where it is already mounted and maximising the slack for the last bit).
Another tip is to have a little bit of air in the tube so that is holds shape, and then using the end of a tyre lever to poke the puffy bits well into the tyre as you go. You can also try wetting the end of a plastic tyre lever and sliding it along the rim, rather than using the normal bending action – but expect to lose some knuckle skin if you try that one.