how do i limit my search to long term boarding - not seeing a filter for that?

I'd recommend two alternatives.

1. If your time is limited, call Rover support. They have access to additional filtering criteria. - or-
2. Enter both the beginning & ending dates. This will filter out some sitter whose calendars indicate not available. I just tried it out, and without zooming into the map, by entering July 31, 2018 - May 2019, there were 16 pages of sitter profiles versus when I entered July 31- August 1, there were twice as many - 32 pages (20/page). So, you'll likely want to use other filters available, such adjusting the slider bar to indicate how much you're budgeting per night, using the + sign to zoom the map to make your search more reasonable, and any other factors that matter to you would likely also help yield a more reasonable number of profiles to review. In your message to sitters you're interested in, state the length (approx. dates). When you meet the sitter, you can discuss the booking details. It's simplest to book (and re-book) monthly, as you would get charged at the time of each booking and the sitter gets paid after each increment, but you & the sitter may agree to some other frequency.

There is no filter or way to search for sitters who would accept such a lengthy visit. You might actually do better working with a rescue group to find someone to foster a special-needs dog.

Add: I've thought of a workaround perhaps for using Rover. When you search, put in the first month of boarding dates and see what comes up. If you do get any sitters from that search, discuss your needs with them. The bookings would be for a month each in duration. That way the sitter would get paid on a regular basis and you would continue to book the sitter through May of next year.