Sorry. As a sitter I don’t know exactly what you can see as an owner, I am not sure if you can invite more than one sitter at a time but if one accepts I think then the sit is confirmed. Anyway, from my own experience and from what I’ve read on this forum, most sittings are agreed via applications rather than by owners invitations. You can message the sitters that have saved your listing but if they have not applied this would probably mean that they are not available or are considering several options and have not made up their minds but you have nothing to lose by asking.
There are several threads about invitations that may be helpful
(Can HOs invite sitters without opening their profiles?)
What's up with all the invites?
Good luck with your listing.