If/when the home appreciates enough, you can refinance to eliminate the PMI

Some of the new apps and cards that you can just tap against the card machine reduce or eliminate the extra contact.Collectively the federal government (Treasury, Federal REserve, DOJ) have been trying to limit and/or eliminate it for years.  

A trust would be a wise move as well, if you're very concerned about your identity, but I would start by ensuring all the LLC info was buttoned up and minimize (eliminate) interaction with the tenants. 

I eliminate dreamers, schemers, and those with unrealistic expectations.The second area where you provide a lot of value is in your strategy.

Goal is to eliminate  vacancy if possible.

One property management firm around here was so uncooperative that I have eliminated ever hiring them for my properties. 

There are other FHA requirements concerning which you should contact your local lender, but determining whether or not a triplex or fourplex meets the self-sufficiency rule is a good place to start as this rule will immediately eliminate many properties from your search, especially in expensive markets like ours.Good luck and reach out to me with any questions!

It doesn't eliminate all but id say it helped a good decent amount.

You could also probably refinance under a conventional residential loan and eliminate your PMI if you really have 35%+ equity.

Start with the max price you can afford and eliminate any cities that don't make sense based on your budget.