This was very unexpected for me as the current tenant informed me about her situation very last minute and after the fact.

I doubt any replacement builder would commit to timeframes as there's a lot of variables and several unexpected product shortages.

Long story short, we purchased a house this year for a family member to live in, but they passed away unexpectedly before they could move in.

My main fear is expanding too quickly and if I have a vacancy or something unexpected with one of the properties I don't want to be sitting on multiple mortgages I can't pay.

As long as you have access to a lot of capital to fund renovations, vacancy, and unexpected items, not to mention can handle the stress,  and trust me--t will be a lot, and it's a lot of stuff no one  (except BP!)

Keep cash on hand and hide it somewhere safe for all of the unexpected issues coming your way. 

The last home inspection I did I got several safety hazard warnings show up due to not having the appropriate GFCI outlets in the right place.

If they are late, talk to them-- maybe they had unexpected medical bills, maybe a funeral, maybe a car accident/problems?   

If its a strong fishy smell, check outlets and places to plug things in.

I ordered the dehumidifiers and scheduled an install with my contractor as there needed to be electrical outlets to be installed.