Utilize Approved PTO for Overlap Pay; Be Aware of Potential Relationship Burn.
Your strategy to use 30 hours of approved PTO from your old job while starting a new one is a smart way to get that 'double-pay' effect, which can be a financial boost during this transition. It seems there's no clear policy for PTO payout when you leave, so this could work in your favor.
How: Make sure your PTO is formally approved before you resign or on your last day at the old company. During this approved time off, you can do other things, like start your new job. Since you don't care much about references or relationships with your current employer, the main thing to consider is that quitting right after taking vacation is generally seen as unprofessional and will likely burn bridges with your former employer. But it sounds like you're okay with that.
Expected Benefits: An extra $1000-2000 (as you estimated) from the overlapping pay during your PTO.