I think asking for a specific few minutes (and then leaving) may be fine, but realize they may not want you to be there the whole time.
When I was president, I initially wanted to attend the staff meeting to enhance communication. Our principal, with whom we had a GREAT relationship, was very resistant.
After I thought about it, I understood. A staff meeting is an internal event. Most of it is routine, but they need the security of being able to candidly discuss sensitive issues and problems without an "outsider" present.
Maybe you can fix the bad blood now that the old President is gone?
I see no reason to not try and reach out to them to rectify the situation. Try attending their meeting to speak to them or write them a letter and put it in their mailboxes.
We have 2 teacher reps each year and they take turns and switch every year. We do not ever ask them to get up and speak about anything. They just come and listen and they aks questions or we bounce ideas off of them. Just a thought...maybe they don't like to have to prepare something to have to get up and speak about? Maybe doing away with that will be easier in getting them involved?
The best way to know is ask them? Another idea would be to go and personally speak to one of the teachers who carries the most clout and ask them their opinion on how you can remedy the situation?
Also at the end of the year we also buy the two teachers a gifts to thank them for serving as the rep that year.
Like other schools, our school has a problem with low teacher attendance at our PTO meetings. And while I agree it can become disheartening - it was handled quite poorly by our previous president. (Every month at our membership meetings she would make a big scene when we came upon the "Teacher Representative Speaks" item of our agenda. Knowing very well there was not a teacher present she would announce "Now we will hear from our Teacher Representative. But, wait . . . wait just a minute. Huh, it seems AGAIN this month we have no teacher representative. NEXT ITEM ON THE AGENDA!!")
After awhile I think this began to cause a rift between the parents and teachers - and defintely didn't encourage them to start coming.
Anyway, I am brainstorming of some ways to close the gap between us and was thinking about requesting 5 minutes with the Teachers at a monthly staff meeting. Just to communicate projects and thanks to them and to talk about new projects they would like to see. I am wondering if anyone has tried this, and if so, if it is successful. Thanks for any input!