WE're going doing the same trip from FL to MT at the end of May. But we are continuing on to Alaska from there. The fact is that here in the flatlands we are at less than 300 ft and St Mary outside Glacier is almost at 5000 ft. And inside the park you find spots at 10,000 or more so you are just going to have to adjust to mountain driving.
Frankly the winds have never been much of a concern. The switchback roads will occupy your attention. I find driving thru St Louis, which as far as we are concerned is the worst city to drive thru, much more stressful than mountain driving. The worst wind we ever encountered in 30 years of taking summer trips was in California around Death Valley. Not the mountains. They get dust storms so bad that the wind strips paint off of vehicles.
So relax and enjoy the trip. Staying on Interstates as other recommend will avoid the worst of the roads.
