Hello, is it possible to set a limit on how many premium listing slots are available? So that after that number of premiums are paid for, the premium option is no longer available until one or more of the existing premium ads expire or is removed? I want to show only a set number of premiums on my home page. But I also want to make sure that people don't keep paying for premium after the maximum number of premium slots on my home page is met.

That is not possible.
If you have more premiums than slots, they should start showing in random order.
Basically it is terrible plan to stop monetization in such way, better to increase price to keep it in balance.

I tried it and they do not show in random order after they exceed number of slots. Rather, most recent ones show. Is there a way to make them show in random order that I am missing?

Pick is random, but always same random.
Anyway this has nothing to do with plugin.

ok great. Thank you