I've applied for a conventional loan: 3 units, owner occupied, NJ, 5% down.I have enough W2 income to cover the loan and additionally, there are two units rented already. 

The last financial advisor told me securities based loans are close to a conventional loan's rate.

Then when it is complete, have property appraised and refinanced to pay back the hard loan from my Mother or other lender and because I overfunded, receive cashback at closing and either pay back into the new loan or wait for another deal once I get renter in on this place with me.My hiccups will be my income to qualify for the new loan, and the fact that I have an existing mortgage which affects my DTI right out the gate.

I know that going on the loan in my own name would allow me to put more loans under my belt in the future before we get married and become one unit. 

However, you're referring to Fannie Mae's 5% down loan program for OWNER OCCUPIED 2-4 unit properties.

If not - you are bringing cash to closing just to get out of the loans you already have.

It is just more labor intensive in general.

If your loan was in fact an FHA loan when you acquired the property, that may be what you're running into. 

Looking for advice on whether I should take out the equity, or seek another type of loan.

I’m assuming you can only have 1 second home loan at a time?