Need Help Structuring First Deal (Cash out refinance analysis)

[MJ Courter]

Good Evening BiggerPockets community,

I have been spending the past couple months in the education/research phase of getting into real estate investing and getting ready to purchase my first property. I feel like i can analyze basic deals (BRRR/rentals/fix and flip) but I am trying to get a little more creative to fund my first deal.

Here's the situation - I purchased my home nearly 10 years ago and the current loan payoff is right at 100k. The value on my house based on comparables and feedback from an appraiser and some real estate contacts in my network put the value at 180k now.

I am looking at a 2 bed 1 bath HUD property (available to owner occupants only) in a B neighborhood with an asking price of 44k. It needs some cosmetic fixes but no major issues. I've had several contractors out with me to look at the property and it looks like rehabs will run about 15k. ARV about 120k.

To recap:

Current home => 100k owed and 180k value.

Opportunity => 44k asking, 120k ARV, 15k in rehab costs.

What I am thinking of doing is a cash out refinance to fund the downpayment on a 20% conventional loan and the rehab costs and live in the property for required amount of time while renting out my current residence. My current home would probably rent for about 1200-1300/month but it is pretty much rent ready all over save some fresh coats of paint and a cleaning.

Now I am at the point where I am stuck on the analysis because i would be using my current residence as the rental and living at the flip. To me it seems like a good deal due to the equity gained at purchase but my current home is probably not an optimal rental based on how much the new mortgage after the cash out refinance.  Am I making this more complicated than it needs to be? Any feedback on how i could better structure this would be greatly appreciated. I really don't want to give up and go back to watching dancing with the stars ;)