Your home equity = your property's value minus your loan balance. So even if that value is currently negative, every dollar you pay towards principal increases it. It's not an expense.
Your expense is that you've hitched yourself to an oversized loan, so you're putting money from one pocket to another, except the latter has a hole in it and you have an obligation to keep feeding it.
If your cost was only mortgage interest, you'd be happier with 600k outstanding at 1% than 300k at 4% for the same house.