Figured I'd throw my thoughts on this: I was in a similar situation.
"My company" had lost it's largest customer (a hospital that decided to transition to in-house talent.) We went from ~25 employees to ~5 over the course of a year (when I left for my current job about 4 months ago). I stayed while the company shed unneeded baggage (couple useless people, some with skills no longer relevant, some wanting more pay than affordable, etc). I was kept on because I was versatile and at the bottom of the pay scale.
But I started searching. I updated my LinkedIn. Kept in contact with recruiters that seemed interested. Went on a few interviews. Finally got the job where I'm at now.
I kept getting experience. Left on good terms. No time off between jobs.
So my question is, as I posted in my comment: Why does it have to be either/or - black/white - options?
- I kept the full time job despite not getting a pay raise for the last 18 months.
- I didn't have the "late" paychecks you did, but I know there were issues making payroll.
- During that time, as people kept getting whiddled away, I was doing my job to my utmost but didn't hesitate to look.
- I have more than a couple "sick"/"vacation" days that were used to interview.
- My Co-worker went to 3.5 days a week (I couldn't afford that, but he didn't have issues).
At the very least, you need to expand your network and keep the options open for a good opportunity. Worst case #1: You waste time, the company pulls through and you stay at your current job. Worst case #2: Company folds and you are left without a job... for months... which makes it harder to get the next one.