First, try not to worry too much until you see the whites of their ... contracts. Rumors are sometimes right, but that's often an exception. Maybe you should go for a bike ride?

If it does play out as you've outlined, look carefully at the details and your options. For example, how long does the no-compete clause hold? I'd expect "forever" to make (your) lawyers salivate. If it's for, say, a year, well, maintain your contacts. Even if it's for longer than your paid time off (15 months), I suspect they won't care if you let three months or so pass before you start working. As others have mentioned, non-compete clauses are rarely worth the paper they're written on.

Never disclose proprietary information, of course. That goes without saying.

Finally, I'd think hard about taking the "terminal leave" option, with benefits, over the lump sum payout. Take three months, do a TransAm tour, keep working your contacts via email, then come home and get back to work!