Avis/Budget share fleets in most locations. Please see this thread for Avis.

Other SUVs in the same category as the Escape are:
Hyundai Tuscan
Kia Sorrento
Kia Sportage
Nissan Rogue
Subaru Forrester
Subaru Outback
Toyota Rav4
Volkswagen Tiguan

Most of these are rare to see these days except the Escape or maybe an Outback or Sorrento. I would suggest looking for an upscale Escape and specifically asking for that spot #. However, if their lot isn't full of midsize SUVs, you might be able to talk yourself into an Edge, Cherokee (Avis has VERY nice ones), an FJ Cruiser or maybe even an Explorer from 1 class up.