I’ve been on Whitney and Shasta dozens of times by various routes. When the Mountaineers’ Route has unavoidable snow and ice, it’s comparable to the steeper sections on Avalanche Gulch. The difference is that the MR has quite a bit of rock climbing that you don’t get on Shasta. Below the notch, the rock climbing is pretty easy – mostly class 2 with short sections where you’ll do a few class 3 moves. The “Final 400” above the notch is fairly sustained class 3 with harder possibilities if you get off route. The Final 400 can get treacherous where the snow melts and refreezes as water ice. If your rock skills are as good as your snow and ice skills, you should be fine.