This had to be frustrating. If I could give a little perspective from the client's point of view: I've worked in property management for 5 years, 3 of which were for a company that used Ellis. There are two reasons why Ellis and subsequently the client are so particular about this.
1. leasing agents are often trained to handle/track all their leads from initial contact all the way through to closing. Passing leads/appointments off to co-workers can be seen as not taking responsibility for their work. Impromptu or last minute visits are one thing, but if you're speaking with a leasing agent in the morning to do an afternoon shop that day and he/she is making every excuse to not be the one to meet with you although they'll be there, the client will likely want to know, so make sure you share that in your notes.
2. If the client is asking for a particular target it is likely for a good reason. i.e.: they've had a poor shop recently and they want to see if the employee has learned from the mistakes or this shop could be the verification of positive or negative performance the company is looking at in that employee.
If I could give a tip on getting leasing agents to follow through with you from phone call to appointment, I would say, make it clear to them that you've built a rapport and feel comfortable only with them. If your schedule permits, specifically ask the target for an appointment when they know they will be available for you.
"I feel like you really understand what I'm looking for. I'd love to set up an appointment, is there anyway I can make sure to come in when you're available?"
I hope this helps and I hope to have good experiences seeing things from the shoppers point of view!