What he said about AMPs. AAMPs usually require less information (screening/references) and are pretty no nonsense about slotting you in. The downside is the PO's can be hard to get a hold of, and aren't always real good about calling back. Emailing - the best way to avoid phone tag - usually is not an option unless you are regular to them.
Escorts may take a little more back and forth as their schedules are more fluid, they may want to pre-screen you (LE) or ask for references.
I don't have the time but can plan in advance, so I always try to do it through email. For me, way more efficient than playing phone tag, going through the awkward dance on the phone, etc. Providers who read email and are willing to do everything via email save me a ton of time. The first time I speak with them is to tell them I am in their neighborhood and get final directions.