You need to be under 5/24 to be approved for the CIP, but the CIP does not count against a 5/24 slot. When you're back under 5/24, apply for the CIP. No need to double dip with a CSP if you're worried about meeting the MSR on both cards at the same time, because the CIP won't count against 5/24 and you can apply for the CSP later while still at 4/24 (and maybe double dip then). I've also seen mixed DPs on how soon to apply after a card drops off 24 months, so I can't comment on that.
Just a little background on my CIP application because it sounds a lot like your situation. I did some contracting work between 2013-15, made some money, filed 1099-MISCs, paid taxes. Earlier this year, I was chatting with some old clients who asked if I might be interested in starting up again as they may have some projects for me. That was the basis of my CIP app: resuming my contracting work was my business. I didn't have any business income at the time or from the previous year that I could use, and it didn't feel right about reaching back to 2015 (although I suppose you could make a case for using past income as an estimate). I just applied with my annual salary in the same line of work, total household income, and counted my prior contracting work for a total of 4 years in business. My application went pending, but I was approved after a few days.
If I had to recon with Chase, I would have told them that I did independent contract work a few years ago, and I've had some old clients reach out to me with new opportunities that I'm very interested in pursuing; I need a business card to keep business expenses separate; I have a longtime banking relationship with Chase and the CIP sounds like the perfect card for me; yes I don't have any current income from resuming my business, but I did make money in previous years (and can show proof if requested), and I have personal assets I can rely on if needed to settle business debts. Luckily, it didn't come to that.
Here are some helpful blogs:
https://millionmilesecrets.com/2011/06/09/3-ways-you-may-qualify-for-a-business-credit-card/
https://millionmilesecrets.com/2012/12/12/chase-business-credit-card-application/
Good luck!