You could always consider more itm puts for fewer contracts, and generally that sort of a deeper itm ratio roll uses lesser margin in my experience with IBKR.
Obviously going with a single short 1600 put or something like that is also an option. But that could be early exercised unless you have a few months to expiry.
In your situation, what I'd do is warehouse the exposure in 3 or so 1200 puts 6 months out. Then when the time is right and there's more macro clarity, take one put at a time, flip them to a handful of bps and grind them out.
And I screwed the math up again...I was using the NET premium from the roll, I suspect the margin calc uses the FULL premium from the new position.
So then it'd be quite a bit more than I thought.
For example July $1200 would be $180 underlying 20% plus $309 ITM plus $330 premium, so $81,900 per contract margin needed.
So going back to the using 10 spreads for easy math-
Selling all 10 long puts only raises 25k. Releasing the spread margin on all 10 gets you 110k. NET credit on 10 new $1200 July puts is 220k.
Which adds up to 355k. But margin needed for 10 of those $1200 Julys is $819,000.
If I only sold 5 of them I'd need 409.5k margin. But I'd also:
Raise 110k less in new net credit premium
Have to BTC the remaining 5 original short puts at 64k.
Meaning I'm needing 409.5k new backing, but only raising 181k.
Dropping new contracts to only 3 would drop needed backing to ~246k. But I'd raise 44k less premium and have to BTC 2 more contracts at 25.6k, so now I'm only raising about 111.4k.
So either I'm still badly misunderstanding some math, or this doesn't appear to be a solution as I'm perpetually short more than half the $ needed?
EDIT- Just for completeness I did the math (I think?) on the one $1600 put you suggested.
I net $58,000 credit (full premium is $709). Backing needed is $180 plus $709 (ITM) plus $709) premium... which leaves you needing $1598 to back a $1600 put.
Which kind of makes sense with how insanely DITM that is.
But doesn't seem to help much, I'd need 159.8k to back that, and 198k to BTC the 9 other short puts, and only net 58k credit plus 25k selling the long puts.