Do the usual stuff; inspection, financials, leases, rent roll, and  any agreement with the seller have your RE savvy lawyer read every word with you and explain every intent.

Where we’re having difficulties is in getting in touch with these owners and we are looking for suggestions as to the most cost-effective method of tracking down phone numbers for these absentee owners?

Luckily the claim was bogus (medical records proved it) but the owner had to pay for the lawyer in the Workers Comp. case and that cost thousands..My advised would be to have anyone who works on your property show you proof of Liability Insurance and Workers Comp.

For routine legal work, he may not be cost effective. 

Our lawyer said if we switch out the lock, we have to leave her a key until her 7 days expires.

I have had mice and rat issues and spent thousands on exterminators only to realize its more effective to seal the holes and monitor the area. 

Since I'm not a lawyer and I don't know what state you're in, you'll need to find out if this property passed to this guy automatically because a living trust was in place, or if it needs to go through probate before he gets it, or if he was a joint owner with the sister.If all this is clean, then you should be able to buy it from the guy.

The effective property tax rate of both states was ~0.8%. 

Two CEOs later the actions taken before has a pronounced effect on the corporation even to this date.

I have monitoring traps up there, but I am not sure how effective they are if there aren’t many bugs.