Hi - sorry about your difficulties with the lawn and garden hotline. We will look into this. Sometimes, if you don't get through and are able to leave a message, someone should return your call. Please understand that these are both 'free' resources.
As for transplanting lilacs, I would wait until spring now as you'd like at least 2-3 months for transplants (especially if they are bare root) to root in before the ground freezes. 
You can cut your peonies back now or wait until spring (especially if they didn't have any disease issues). Most of the plant's energy has gone back into the tubers (rhizomes) by now, so it's a personal choice whether you'd like to keep the top growth for any winter interest, i.e., snow collecting, etc.

Thank you for contacting us.

Well, my initial response to your first paragraph is how can you leave a message when you are not able to get through???? All it does, and for more than a half hour at a time, is buzz (the noise you hear when a fax is being sent).  So the call is never picked up by you!!!

Hello Elaine,

I’m sorry about the confusion over the hot line and I understand your frustration. I wonder if you have the most recent number which is:<personal data hidden>.The hot line is operated Mondays, Wednesdays and Fridays, 9-12 and 1-4. That number was picked up when I just called.

With respect to your lilacs, late winter to early spring is ideal. Read more about planting and caring for lilacs here: https://arboretum.harvard.edu/events-2/lilacs-at-the-arnold-arboretum/lilacs-read-more/

As previously advised, peonies can be cut back now because they are dormant.

Thank you for contacting Ask Extension.

Yes, that is the number I called.

Well Elaine, I'm very sorry for the mix-up.