Is there any Madison venue that can be booked for daytime--not overnight? Large cities do that, but can not find anywhere in Madison area.

I really think you would not want to stay in those sort of motels. You may also be calling attention to self by calling and asking them such questions. IMO

To some quickie places that's their bread and butter.

And what are the quickie places?

Cant help with Madison. Several down in Chicago area. Doubt you'll be coming down here. What I've done in the past to avoid a phone call is to just go up to the desk and ask. They cant arrest you for asking.