Unless you're a good C++ coder, the only solution would be to use Godot 1.0 which still had the gles1 renderer next to the gles2 one. You'd have to build https://github.com/godotengine/godot/tree/1.0 from source yourself, and experiment with it to see if you can have it select the gles1 renderer (there might be a command line option for that if not done automatically).
If you are a good C++ coder, you could readd the
drivers/gles1 folder from 1.0 in the current master branch or 2.0 branch, and try to tweak it to make it work with the recent Godot versions.
But the best solution is still to let OpenGL 1.4 go, and find a better GPU. I'm sure you can find GPUs with OpenGL 2.1+ support for $20.