Do you have a copy of Gordon Edwards, climbing Glacier park? A must read!
Considering the time of year, and climbing solo, this would be my list of favorites.
#1 Mt Jackson, 10 to 12 hours, class 3. A cruiser trail to Gunsight lake, climbs very well with snow (take an ice ax) awesome views to Blackfoot, and Harrison glacier.
#2 Mt Edwards west ridge (classic) some short easy 5th class,mostly 3 class, seldom climbed route, but has some of the
best rock in the park, standard route down.
#3 Mt rockwell, great fourth class finish!! many trail miles, long day, Likely to have less snow.
#4 Rising wolf, south face, 3 class, minimal snow, shorter day.
#5 going to the sun mountain 4 class shorter day.
Here are a few other great climbs, that I personally would not climb solo.
#6 Mt. Wilbur, thin mans pleasure, 5 class, A must climb!
#7 Split peak, 5 class finish, great rock, rappel the back side. (solo???)
#8 Blackfoot mountain Awesome climb, can be done in a very long day, glaciers, ice falls, crevasses.
Other fantastic climbs, that would be better in later season, Heavens peak, Kintla, Cleveland, Kinnerly, little matterhorn.