> Unfortunately custom projects and the like won't work for teaching fundamental maths skills.
I am not sure I agree. One of the projects I did for my projective geometry class was to do an inverse of a projected drawing (in AutoCAD) and save a 3D .obj file. In differential equations course, I was given a project to prove a theorem that is generally missing from the school books (or usually given as an exercise). You can also let people devise proofs in a closed system of axioms and a few theorems.
It is a hard and different type of work, but I am certain you can both teach and get to know students with theoretical math projects. If they get someone else to do it for them, yet they are able to present it in front of the class (online) convincingly, they have likely understood the concepts, which is what teaching is all about.
[1] There's quite a bit of research on this. Bretag is a key author.