I was sufficiently deep ITM on those puts that I was typically rolling 1 week before expiration. I was definitely rolling more than 2 days before expiration.
My trigger / decision point was the time value. As that approaches 0 and as DTE approaches the likelihood of early assignment increases. I was deep enough in the doodoo that the early roll made me comfortable I would avoid early assignment. I was also typically rolling 2 weeks at a time, and even rolled 4 weeks once. My thought process on those was that I was completely dependent on a big share price move in my favor and I was far enough ITM that needing a week to get all of that back didn't sound unlikely. That 4 week roll also didn't budge the strike
Most of the rolls were getting me $1-2 credits for a 2 week roll. I mentally round those to 0 but of course that isn't actually 0. There was one memorable roll for $0.02 because the commissions made a $0.01 roll into a net debit.
The BPS cure is, I think, reasonably straightforward to describe. Using a single $760 strike put that has $76k cash backing it, assuming a cash secured put. I changed that into 4 $200 BPS which used $80k cash (margin) to back them. I also tested changing into 8 $100 put credit spreads but the resulting short put wasn't much different.
Those 4 spreads got me to a dramatically better short put strike. Something like changing those $760 strike puts into 460/660 strike put credit spreads. I also pulled in the expiration by a week (nearly no difference keeping the expiration the same). The new position was still ITM but by $20 or so instead of $120ish.
I was expecting I would need to roll the spreads a few times to finish resolving them, but the shares had a friendly move for me and I closed that mess out the week that I rolled.
There are a few things going into why this worked.
1) Changing from 1 csp to 4 BPS (put credit spread) added leverage to the position.
2) That increased my rate of gain from share price moves in my favor, as well as enhanced my rate of loss for share price moves against me.
3) Most importantly - it got my strike back into the land of significant time value so I became exposed to both share price moves in my favor as well as time decay in my favor. The previous position never had very much time value, so there was very little time decay value to be had.
The risk here, and why I went with such a very large spread size ($200) was if the shares had fallen dramatically. Say $640 at roll time, down to $540. In that case I would have ended up at $120 ITM (where I started) except then I would have had a 4x increase in the number of those ITM positions, increasing the size of the loss by 4x. I felt that was a good risk to take, but it was on the table.
Leverage gains also means that leveraged losses are on the table. I believe that the real value was putting significant time value back into play, and is what would have gotten me to resolution with a few weeks.