The parents are adults, so I doubt you will have much "Why not me?' whining. Definitely invite a dad or 2 to help out. I say 2 because it might be a lot of work for just 1 dad!

If it were me, I would extend an invitation that saying that you will be glad to provide transportation for the child. However, if a parent would like to accompany his/her child, the cost is $_.00 per adult. Chances are, you will get many takers and won't have to worry about it. No one else needs to know who you paid for, and who paid for themselves. Go for the sleepover, but have them be discreet.
I always take my DS into the ladies room if DH isn't around. If other women have a problem with it, TOUGH!! He is my child, and his safety is more important than their sensibilities! I don't make him hide in a stall or stare at the wall because all there is to see are sinks and stalls. We make it a non-issue. A few years back, in my small town, a 9 yr old boy went to the park with his Grandma. She let him go to the mens room by himself, while she waited by the door. A 14 yr old came and went. She began to wory, and went to check on him. The 14 yr old had slammed his head against the sink and floor until he killed the kid... because he was curious as to what it would feel like. Just pointing out that you neber know what sickos are lurking around.