The home would sell for around 460k right now with minimal repairs needed.

It's a bit of a costly repair relative to the price of the fridge - they need to be replaced for around $500.

I myself have done much of the repairs and have helped him with these properties for over 20 years.

But you need to learn all about landlord/tenant laws, how to do basic repairs, know what average labor and material costs are for common projects. learn about payment systems, how to interview property managers, tenants and handyman services, build a team of realtors, contractors, title, hard/private money lenders, inspectors, appraisers and soooo much more. 

The amount of work and repairs that go into it may never catch up for you if you are maxed out on renovation budget.

I want to keep it in the family (my grandparents originally bought it in 1957), but I’m unsure about the best way to move forward with the repairs.

I would think a detection device would be easy to fool or disable, and difficult to prove in court.I would focus on inspections and look for the following evidence, then document with pictures, written warnings, demands of cleaning/repairs, and follow-up inspections.

Because of your loan size, I would advise to buy the rate down using up to 2 points as those usually have the quickest ROI for the payment savings and you will not see rates drop low enough probably to do a refinance that makes since as it would take longer to recoup the cost of the refinance.HomeStyle Renovation loan does require all work be done by a GC so you cannot help with the repairs. 

A CPA can make sure you maximize those benefits (like depreciation, mortgage interest, repairs, PAL, etc.) and avoid costly mistakes.

The worst of them refuse to make repairs to 100 year-old buildings, creating a slum lord problem and giving all of us a bad name in the eye of the public.