If you're shooting a lot of stage performances, this does often necessitate a fixed or limited shooting position. I shoot a lot of stage, and wouldn't be without my zooms. I run with a 70-200 f/2.8isII on a 5D MkIV and a 24-70 f/2.8II on a 1DX. The flexibility a zoom gives to recompose from wide to a tight shot of a principal or point of interest isn't something I'd be keen to give away. I trust both these lenses at f/2.8.
If it came to a toss-up between the brightness benefits of a 85 f/1.8 or 135 f/2 vs the flexibility of the zooms, I'd go with the f/2.8 zooms every time. Even if that means cranking the iso way up which the 5DIV and 1DX handle surprisingly well. At a recent job I ran both bodies at 12,800 iso as I needed to freeze high energy action and dance moves, something that needed shutter speeds above 1/500th and preferably 1/1000th. It was as fast moving as basketball. Shoot RAW then a touch of NR in post and you'll have happy clients.
OP you're in a slightly more difficult position shooting with a crop sensor body. I also have a 7DII which would deliver very similar output to your 70D, and I'm generally reluctant to push that past 3200 iso, or 6400 iso at a pinch depending on the requirements of the project.
-pw