Yes, crampons on steep terrain really are that much slower than trail runners on dirt. I'm also not sure if you're accounting for the effects of altitude? (Even with acclimation, there's a big difference between the times I can pull off in the Presidentials of New England vs. the volcanoes of the PNW.)
Some of my ski mountaineering trips follow a sequence of:
– trail runners on dirt
– lightweight Dynafit setup "skinning" on moderate snow
– aluminum crampons up steep snow, which is far slower than the previous modes of travel
Depending on the time of year, taking the standard Avalanche Gulch route up Shasta might entail:
– a quick trail run up to Horse Camp on very casual terrain
– slower travel up moderate snow pitches to Lake Helen
– much more careful crampon & ice axe work up to the summit on pitches up to about 40 degrees, where you really don't want to rush your travel
Strongly consider taking a basic course in self-arrest etc — you don't want to use crampons & ice axe for the first time above Lake Helen. I'm also not sure you want to be up there with that kind of hiking boot, although I don't know its detailed specs. Nevertheless, there are more lightweight alternatives to the typical plastic climbing boots seen on Shasta, which would be required for something more ambitious like Rainier, but aren't necessary for a daytrip on Shasta. I'd also recommend an aluminum crampon (assuming you're not going out of your way to take one of the few more technical routes) — all the other climbers will have steel, but my aluminum crampons have been fine for numerous trips on Shasta. Aluminum crampons will get dull more quickly from rocks (i.e., "mixed terrain"), but it's not like you're planning on doing highly technical steep climbing where you'll encounter ice & rocks, so alu should be fine. Just stay far away from Kahtoolas (steel or alu): their front points are insufficient even for Shasta.
