Sat is a day where I have some time for fun.

Most providers like at least 24-48H advance notice. The other option is to pre-screen and get approved by a few providers on your radar. That way, if pre-planning isn’t your forte and you’re prone to last minute requests, half the battle is already complete.

My occupation doesn’t allow that time of forward thinking.

I would have been glad to see you.

If you pre-screen with the providers you're interested in and you get the "green light" that means when you do have the time, you already have a list of people you're vetted with and approved to visit, therefore increasing your chances of an appointment.

If you explain your circumstances and get the screening done ahead of time you should be able to find some providers who will help you out.