What you want to do is a "cash out refinance". That's as opposed to a "rate and term refi" where you are paying off an existing loan.
There are seasoning issues with either. The last one I did closed in late November. It was purely cash out. Actually, I had to bring $1000 to the closing. I had to wait six months after the purchase. With a cash out, I think you're going to be stuck waiting at least a year. You'll need good credit (720, I was told when I did mine, a friend was recently told 740), some cash in the bank and enough income to cover the payment. Counting the rental income with make it harder. As is, you're going to have to do some searching to find a lender.
If you're under a year with any FDIC insured institution they will use the price you paid, and maybe the repairs, as the value. Unless an appraisal is lower.
You won't get 90% and even 80% will be very tough. Figure 70%, maybe 75%.
The bank will chose the appraiser. You MUST be there when the appraiser comes. Have your own comps. Have a list of repairs. Be prepared to point out everything you did to the place. As you're planning this out, be very pessimistic about comps. If you pick the highest comps, you're going to be sorely disappointed. The appraiser won't. What you want to try to do is to keep him or her from picking the lowest comps.