It seems like there are some trusts or other funding programs that consider contributing to restoration and repair projects, but we'd like to operate on the assumption that we will not be chosen for these types of grants, just in case.

If the ARV is $135k, you should be paying around $75k at the most for the house if you plan to flip it (I'm making a assumption that about $20k worth of work is needed based on your post)If you plan to hold as a rental you can pay a little bit more, but I still wouldn't want to pay more than $90k for the house.Seems like "no deal" to me.

My assumption is those are foundational issues and not cosmetic.

So using your numbers and making some assumptions: the old house is worth let's say $400k and you owe $225k (almost double the mortgage).

Now make a similar assumption for the debt you are paying down.Not to mention in a few years, you can likely refi and redeploy capital. 

Call and ask them if they will permit the loan assumption for your new buyer if they simultaneously secure a 2nd mortgage or HELOC up to X% CLTV.

I feel like a theme of mine is “jack of all trades, master of none” and worried that might hold me back if I didn’t master one first, then move to the next Both assumptions are wrong. 

Nothing I look at has any hope of being a cash flow positive rental under even the best assumptions, and even appreciation is unlikely to correct that in the next 3-5 years.

Having a good hard money lender would be a wayyyyy simpler process to get it done.If you shoot over the rental assumptions and what you think you could rent the units for, I can plug that in and show you what it might look like.

Try laying out some of your assumptions in a deal analyzer and we can give you some better insights.