HOWEVER, I am doing everything I can to ensure the problem is not with the house (as much for my sake as theirs, because it's not going to do me a damned bit of good to have them pay for it if it's going to keep happening).They have turned this incident into a reason NEVER to pay for anything.

It sounds like you've already taken the proper first steps, which are to learn as much as you can and then to define your investing strategy.Your dollar will certainly go further in the Phoenix metro area than it will in Orange County, and there are numerous 2-4 unit multi-family properties in Phoenix, Mesa, and other suburbs that are within your budget. 

As a borrower myself here in Southern CA, I have done at least 40 fractionalized notes with lenders and navigating through this process as a lender without experience (not sure what your experience is since it was not mentioned) can also be dangerous without the proper guidance.As David mentioned, $110k in CA is not likely enough to get you in first position without fractionalization.

Make sure you give proper notice to discontinue the lease at the end of June, most states is 30 days unless expressly noted in the lease language. 

I feel it will be tricky to find financing that early but hopefully I build proper connections and create a game plan that investors will feel confident with the deals I will successfully make profitable. 

Is there anything specific I should be asking/saying to them (maybe to put some pressure on them, but also to ensure that everything will be alright)?

If unsure, always consult a CPA for proper guidance and tax strategies. 

But as with anything, with proper management and teams in place, you can really buy anywhere for the right price. 

So lets dive in and get you up to speed on what's happening; I am currently deployed overseas until mid 2019 with a substantial amount of cash saved up and want to put that towards proper investments while I am away, so when I return home real estate investing will be my sole focus.

I don't do anything in downtown proper, so unaware of any alternatives for people who are into that scene.