I am doing just that with our primary residence. We have alot of equity in it and absolutely do not want to sell. If you do a full refi you will have to pay fees, so do the math on that option carefully, also factor in your higher interest. We're already re-fi'ed at 3.875%. So after researching, we settled on doing a 3.99% variable rate HELOC at 85% LTV. We will use this as the down for 2 rentals OR one SFH purchase if the right deal comes up. I am not sure how well it will work with the amounts you are talking about (60k to 90k value). My lender will go 100%, but above 85% the interest rates climb up pretty fast.
Also consider the cost of the appraisal. I paid $380 for it. I have to factor that in to the cost of getting this money. I was confident that my valuation would come back very high so that fee was nominal in the grand scheme of things.
I am curious what others will say. The rate I have is variable and the market is ever changing. I do have a plan to pay down the amount with our rental income - not just the unit/s we buy, but will likely do the full on ALL rental income pay down sometime after next year, in the mean time we will be paying the interest only payment. We still live on a portion of our working income while our investment income is being recycled and used for investing. Some day sooner than later our investment income will be enough to go FI...but that is still many years away.
Ahh, now keep in mind too that you will need to get your money, put it in the bank and age it 90 days. The lender for your investment property will insist on knowing the source of your funds for down payment and 6 mos. service. I've already told my lender my plans and have emailed them our new HELOC schedule since I will likely be purchasing prior to the 90 day aging most lenders adhere to. I have been pre approved based on the new HELOC.
Lots of details to work through. Make sure your DTI still works out with whatever your HELOC payment will be:) The best of luck to you!