Since then Ive had dozens of calls but only 2 people have shown up for a tour of the property and 4 people have asked for an application.

Someone needs to review your lease and assess the situation in order to give you any kind of advice.

As a regional property manager managing a dozen managers working for me each with a building full of renters I tend to see these things more often and the odd event becomes more normal.

Many pet owners happily agree to this and I assess their income of course to see that this is within their ability to afford. 

Often times in the first contact the prospect asks if there is oil heat,  then they decline to even look at the place.We've done about a dozen conversions to gas heat ranging from about $3,000 to $6,500, some included duct work, gas hot water heaters and central air.

You also have half a dozen people looking at the property simultaneously, creating urgency for them to hurry up and get an application in and their fee paid, since we operate on a first come first serve basis.The other rule I started implementing was that the TENANT/APPLICANT(s) must CALL ME 1 hour before the appointment, otherwise I WOULD NOT be at the property.I was AMAZED by the results..

The question is whats the process to assessing yearly appreciation in my market? 

To see value in a license you probably would want at least a dozen transactions a year.  

Serve the proper notices required for entering the property to assess the situation and do repairs.

You need to have someone assess the joists and subfloor.