I am sure you are doing the math right and obviously, I don't have all the details, but this is what im looking at.
Current NOI: 3686
$300k Mortgage @7.5%: $2098 per month
New NOI: $1588
Rental Portfolio Value: $770k
Rental equity Position: $470k
Portfolio Value and Equity Position if you sold: $385k
If you sold, your NOI would be $1843, so $200 more per month than with the cash-out refi. You are right. You would not have the $100k cash to reinvest, but you would cut your portfolio balance in half and create a lot more work to get it back up to the current value. You mentioned you were going to use BRRRR to build the portfolio, which means you are looking to purchase distressed properties. Unless you are a super experienced renovator and have been managing multiple flips at the same time in the past, having the extra $100k is not all that important. You are likely going to start out by purchasing one property at a time, renovating them, and then stabilizing them, and unless you are looking to purchase in the $700k and up range, you have more than enough equity in the primary to use as your bridge financing through the HELOC... now if you are an experienced rehabber and you want to take down multiple projects at once then the $100k could get you one more property and your velocity of money would then probably be a lot higher.
Ultimately, you have to do what is right for your situation and risk tolerance. But in my opinion, removing the property from the portfolio means that you will then have to do months of work to get back that asset value, and if you are doing the BRRRR strategy, you will be mortgaging the new property once its stabilized and your end game after all the work on your first rehab will be pretty much exactly where you would be if you did the cash-out refi.