The existing house is valued as a negative because it needs to get demolished and has cost to tip the waste or do asbestos remedial work.

As you are asking the question, I would guess that you know that a leaking oil tank can / will open up world of issues; Phase 1, Phase 2, remediation, retesting and who knows what else.You could purchase it subject to all remediation done by the seller and certification of cleanup by the fire dept / county / state (who ever has juristriction on this).Alternativley, you could be willing to invest in the testing / consultants necessary to scope the problem (with no guarrantee that they are 100% correct) and then make offer taking the results into account.Until you know the scope of the problem, you can not know the cost to fix it  so unless you have done this before and have deep pockets, making any offer is very high risk.Oren

Its not cheap to have a property demoed in Detroit, Ex.  2100 sf , two story, between two existing homes will cost approx. 13k, without asbestos and lead remediation - it will take 60-90 days to get utilities terminated, and proper permits issued.

If you renovate then you may need to have the asbestos remediated when you modify the systems using it.

And if he still isn’t satisfied, the appropriate remedy is usually small claims court. 

In answer to your original question, I think you are being more than fair with your suggested remedies. 

We do not currently have the funds to absorb a failure of the heating system, but there's enough income to budget 10k annually for capex and still hit a 10% cap rate, so it's something we could remedy within the first year or two.I reached out to a business contact and asked if he would secure contingency funds in exchange for a percent of AFFO (basically, we'd pay him a portion of the income in exchange for the right to use him as a private lender in the event that one of the systems failed before we replaced it).

IMO it really is a matter of maintenance-both preventive and remedial.

I've never thought of it, but you might contact some local mold remediation companies in your area.  

Get a professional mold remediation bid.