It would be a violation of the agreement and could result in losing my privileges to pull credit, screen for criminal and eviction, etc.

Real estate is a great investment but it's gritty and required time and is stressful.For you I recommend buying a new build condo or town house and renting it out right away or being the financial partner in a joint venture partnership. any other model does not work with your minimal hassle/time/experience expectation. 

Another thought is that you could lose your shirt if the GP fails in their venture or things go sour.

Fix it myself, and lose all that time I could be spending working on the house?

The Housing Authority, in my opinion, wants to control the process by requiring inspection, a 30-day time frame to inspect thus you lose 1-month rent while you wait for them to approve your property.

Philly is a great example of a place where two investors can buy similar properties for similar prices around the corner from each other and one can BRRRR or flip and the other can lose big time trying to do the same.

If you want to buy it in an LLC you will lose most of those benefits.I’m no expert but the Pro’s of owning properties in an LLC do not compare to the pro’s of buying as a personal residence.I’ve done 3 househacks so far and collect via Venmo linked to my personal bank account.

Note, even if insurance pays for all the damage your property suffers, you still lose.

Of course, I'd rather be making money instead of losing money each month.

That's like me telling my weight loss motivator that I don't want to change what I eat but still want to lose this weight.