They mentioned that the rate will be higher if locked for 5-6 months.

I have each unit in the building with a unique rent rate, so even if the tenant does not have the teller enter a note with the deposit (they often do), I still know who the rent payment is from based on the amount. 

I've been with an insurance company in CT, since I started my rental portfolio, but am looking for other options as it seems their rates have been going up and up. 

They're all going to use NOI/PITI, but you'll experience a range of DSCR requirements which will directly affect your max LTV and you'll also experience a range of rates.

However, despite several months of searching, I'm struggling to find properties that break even, especially with current interest rates.

Cash out refinance is usually recommended if you are lowering the interest rate.

I think most investors are feeling the crunch of low inventory, higher prices, and high interest rates.

Obviously you want to pay attention to your interest rates, cost of appraisals, and fees for refinancing.

So your success rate is 0.1%. 

They will hit you on the interest rate and LTV.