Skateboard tape and stick-on rubber mat is a band-aid approach.
The dead-simple and elegant solution to Ovations slipping off the lap while seated (I had a Balladeer many years ago and did this) is to use what's known as a sound-hole guitar strap, like this:
https://qph.fs.quoracdn.net/main-qim...51be86f9fc98-c
There's no way for the guitar to rotate out of position when using this type of strap.
Cheers!