Cash out Refinance / BRRR Question

[Trevor Murphy]

This is my first house hack, and any information or insight is greatly appreciate!

I bought a duplex in the Seattle market for $583,000 with a conventional 30 year home loan 2.99% interest rate with 10% down.

My mortgage is $2800, I'm planning on renting the bottom for $2000 

I am renovating both top and bottom with cash from a Equity Line of Credit I have with my stock portfolio through Morgan Stanley at a 4.5% interest rate.

The total cash ill have into the reno (including labor, materials) is $140,000 ($100,00 of that will be from Morgan Stanley)

My question is if I want to do a Cash Out Refi, is that going to change my original 2.9% interest rate? and if it does would it still be worth doing if my interest rate increases? (lets use 3.5% for a comparable).

And would the better us of the money be to take that equity and re-pay the Morgan Stanley ($100,000) or take the equity and buy another house and use it for the down payment/renovation?

[Trevor Murphy]

@Dave Skow when you say you aren't allowed to "convert" an FHA to a conventional, how would someone go from an FHA to a conventional? Refinance into a 30 year conventional?