I obviously don't know all of the details though.

Normal the price you would be approved for for a single family is not the same as the amount you would be approved for for a 4 plex, although they will probably hesitate giving you a number for a 4 plex without knowing more details about the property you are looking at.  

I think there are some details missing here.

This will be funded by either a cashout refinance or a HELOC on our primary residence, its estimated value is $180,000.

I used to supervise bookkeepers at several companies, and one to two hours a day for what you have is my estimate.

It is time consuming, but I base the interaction off how much detail they put into their listings.  

I did a quick search, and found some people who said they had borrowed against their TSP for real estate investing purposes, but I was wondering if I could pool the hive mind for some more details on the process.When borrowing from the TSP do you arrange it through the TSP or is it a 3rd party lender with the TSP as collateral?

If you want more details DM me. 

You need to understand the buy side, marketing to other investors, estimating repairs and exit for a flip.

I'm also a fan of get the deal first figure out the details later.