With the new information, I will clarify my suggestions. You don't say if you are open to riding lifts, but I added some infor on that just in case.
Stubai: There is not much elevation gain on this drive. You are driving through a valley. However, if you are open to lifts, there are several. The drive is still quite nice. There is a main road with several villages just off it. Some of them might require some walking to truly enjoy them. The road dead ends at the Glacier, but the lift there may be closed. (The summer season started July 1 in 2022. If the snow is heavy, they may still be skiing, but that lift takes you to a little different area on the glacier. They have along winter season which started this year on September 30) Some of the best scenery is between Neustift and the glacier. You will pass through tiny little villages and the most beautiful waterfall is right before the end. It was beautiful in late September, it will be stunning in May!
The tux area could still be wonderful. It is very scenic. After driving through Mayhorfen, watch for the road to Tux. It twists and climbs rapidly. I actually have not driven to the end. (We turned on it accidentally when we should have gone straight out to the end of the valley) It ends at a lift. Since they ski year round at Tux, I know it will be open. For more views, you could take the twisty road up and over Gerlos pass and back. There is a toll for the pass.
The drive to Garmisch over Fern Pass would meet your needs at well. It also climbs and twists up over the border with Germany. The town of Mittenwald is well known for being scenic and quaint. (which also means crowds) Traffic can be an issue (as mentioned in a previous post) We drove it the beginning of October this year and had no problems. May will not be high season. You don't have to do a loop. You could drive as long as you are enjoying it, and go back the way you came. This is a main arterial between Innsbruck and Munich, so it will not be a rural road like some of the other drives.
HInterhornalm (and Walderalm) are the closest to what you have described. The road dead ends at the end. Walderalm was amazing (Hinterhornalm was good but not the same), but it does require the walk.
None of these get you to the top of a mountain, but they all get you to beautiful mountain scenery. Grossglockner is just what you are looking for (particularly if you go out on the road that dead ends at Kaiser Franz Joseph.) This is in the Hohe Tauern National Park. However, it is too far for a day trip and is out of the Tirol. Your original post mentioned you didn't want to go as far as Salzburg. However, with new information I realize that may be because you've been there before. If the distance isn't a problem, a multi day trip with good weather would memorable. If you do go, I would go the recommended route I suggested in my first post (Through Mayhorfen and over Gerlos pass).