I'm having difficulty interpreting your last post. But I "think" I got it now.
For the refi since 55% of the refi is to pay of the original loan, only 55% of the interest can be claimed as a SCH A deduction. The other 45% of interest is just flat out not deductible. Doesn't matter if you figure it at 55%/45% per year, or 55%/45% per month.
Now lets pick of figure of say, 10%. That would be $16,200 of your cash out funds. Now lets say you put that as a down payment on a rental and you close on that rental on Apr 1st,
At the end of 2021 the 1098 you receive from the refi lender shows you paid $10,000 total in interest. 55% of that, or $5,500 is a SCH A itemized deduction for the entire year. 10% of that, or $1,000 is deductible on the SCH E for the entire year. However, you didn't close on the rental property until Apr 1st. So you can't deduct that $1,000 for the entire year. Apr thru Dec is only 9 months. Since you closed on the rental in April that means you can claim 9/12 of that So $1,000 devided by 12 is $83.33 per month. Multipy $83.33 by 9 and you get $749.97. That's all you can claim on the SCH E in that first year you close on the rental. Every year after that, you can claim the full 10% which is $1,000.
As far as that non-existant "reasonable" definition, my suggestion would be to "NEVER" touch that money in savings intended for the down payment. *NOT* *EVER* until you are ready to withdraw the required amount on *the* *day* you make the down payment. That way, I don't see any problem with you showing the "flow" of the money directly from the cashout, into the savings account, and then directly to the down payment on the next rental property.
When it comes to doing what you're planning here, being able to trace the flow of the money is "EVERYTHING". Break that trace in any way, then if the IRS questions it, you will probably lose.
Finally, as a disclaimer, understand that I am not a TurboTax Employee or tax expert by any stretch of the imagination. I do own three rental properties and my primary residence and have 30 plus years experience as a landlord. Over that time I've done my share of mortgages and refi's however. Do be aware that since the 2018 tax law changes I've not mortgaged or refi'd anything. Primarily because of the change in the tax law which says you can only deduct interest based on the "original" loan balance prior to the refi. I am in the process of doing a refi on my primary residence right now, but I"m not cashing out. I just want to refi the outstanding balance because the lower interest rate will lower my payment by just over $300 a month.