Hotel valet service / handicapped spaces

Not sure if I should post this here or under accomodations. . . ..
We will be staying at a hotel with valet service. I read on another site that valet parking "is free of charge to all vehicles displaying a disabilties tag at Disney facilities offering valet service". If this is accurate, how does it work? Do they note down the placard number? Do you feel rushed in transferring for a valet? Or, is it more comfortable to park yourself - so you can slowly exit your vehicle? (We tend to take quite a bit of time.)
When you have special needs -- how much do you need to use the valet? I'm not sure where the handicapped spaces at the hotel are located. The map I saw for Grand Floridian shows the lot across a street -- are the spaces hard to access?

We stayed at the Wilderness Lodge in Dec. and while I was waiting to be directed to where to pull-up so the luggage could be unloaded, the valet glanced in my drivers side window and noticed my HC plaquared (sp?), it hangs from my gear stiff between the front seats. He showed me where to park and followed me over and explained to me that valet parking was complimentary for people with HCs. He even helped my DH assemble my scooter. One day during our stay I had to get something out of my van and they wouldn't hear of my walking over to get it out, my van was brought around and promptly taken back when I got what I needed. I did tip generously and it was a very nice surprise to be offered this service without any charge.