Creating a custom mesh without a probe is possible, you just need to enable it in the correct firmware. If there's a build of Marlin for your machine, check the bed leveling section in the source code, and enable "Manual Mesh" leveling. It'll allow you to Next -> Knob Turn -> Next -- through all 9 points and manually set a bed mesh. No need for a touch probe. You still need to update the firmware to enable it though.
Also don't get caught up in the "BLTouch is for leveling" misinformation. A machine with a mechanical issue will not have the mechanical issue fixed by adding a touch probe, it'll just add yet another source of frustration.
If you have a glass plate and you think it's warped -- you are wrong. Glass is not manufactured that way, and the only way it can be warped is if you're purposely pulling it out of its natural resting state.