Too bad ignorance is not a function of stupidity.  

How should I phrase my interest in the property to avoid coming across as pushy or insensitive?

If the software is not simplifying your life or making you more accurate, you shouldn't use it.Software does have extremely helpful features like online payments, marketing syndication (click a button, and your property is advertised on multiple sites), electronic document review/signing, maintenance tracking, and owner reports.

Pensacola is a great market for investing and the number of properties available right now is up so there are actually some on market properties with potential. 

I've personally done just about every rehab scenario, properties I've lived in, properties bought as investments and even properties bought at auction.You've gotten good advice from folks on this list.

Would a cash out refi be under commercial terms since the property(s) are under LLC?

Secondly, calendar and email functions/apps on computers and smartphones provide great records and a log.

Why hasn't your property manager already answered this question?

For several reasons (property taxes, politics), I would prefer to begin real estate investing somewhere other than locally. 

While it might feel like an extra charge to tenants, these packages often provide value that indirectly benefits the property owner as well—like reduced maintenance calls or ensuring the property is better protected.In my experience managing a large portfolio of properties, these fees are becoming more common due to the thin margins in property management.