It takes trial and error, failing and correcting, eating crap than having to get back up, but the best part is if your in it to really win it, than everything will just be a learning experience. 

Get a small nest egg built up and you can get into a house hack with an FHA loan with 3.5% down.You can do it, just got to hustle!

Might be too risky for my first investment, unless an off market deal pops up as a golden egg, as suggested by @Dan Bernstein.

My objective is to build a nest egg that I won't touch for 20 years or so, and I have a pretty small appetite for risk in this portfolio. 

Unless you hate the rental (I sold 3 of my least faves over the last 11 months) I'd probably keep it.Transaction costs will eat you alive if you sell every few years.

We have worked incredibly hard (7 days a week) and lived very modest (eating beans and rice) to save up $400k cash. 

From what you described the kitchen, bath will eat up the $100K already.

Even long distance REI in not practical because I work long 10-12 hour days and have just enough time to eat and sleep and do it all over again.

The make your own tongue-n-groove type, so when they start eating lunch with you , it means something. 

I would split the cost (or eat it and tell them to get rental insurance and email me proof).