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. The more common thing to be warped is the T-slot rails that your hardware is riding on. If you know anything about aluminum extrusion, you'll know it's pressed through a die, and then kind of bent flat at the factory after it's been extruded.