I believe that we did what you plan to do, back in 1981, with the Sierra Club out of Northern CA. Rather a summit, and back to town in a two day weekend. I've got photos and account details at my PTP website>Peaks Archives>Various Past Peaks..>Shasta via the Hotlum Glacier Sept 1981.
We saw many climbers doing this, serac climbing and ice work, it seemed great for that, then. The TH was nonexistent back then, we just parked our cars as the leader directed, and headed up, no trail or anything.
Just that with global warming or what, you may not get as good conditions as we did. If ice screws will not hold, then you may be done.