We don't know the employer's IP clause. I've certainly worked for companies which claim ownership of only IP directly discovered in the course of doing the comp

We don't know the employer's IP clause. I've certainly worked for companies which claim ownership of only IP directly discovered in the course of doing the company's work, related to the company's work, or using the company's equipment. With that being said, OP is probably doing the work from his employer's office, which is definitely a breach of any employment contract I've ever signed.