Zoia, that's no fun! Ive been there, and it's super uncool. I've enjoyed a rust-free year this year because I (somehow!!) stayed disciplined enough not to buy from milder climes. REALLY wanted to, but didn't.
Thank goodness for meaningful winters. Where I am, the evergreens and sevs don't always die down completely but rust has not overwintered for me even when plants were total rust-buckets. I mulch in spring but don't cover the plants in winter. I know people who have it a bit colder and rust has overwintered under mulch "blankets". I'm sure you are invested in losing the rust without losing plants. I'd suggest allowing leaves and crowns to be exposed but mulching with leaves around the plants because leaves make awesome weed-resisting mulch. Grinding up leaves by using a mulcher or mower may help them stay put around plants, or letting them sit in a pile and get wet and partially decomposed will allow you to mulch with flat clumps around plants (almost like tiling). Best wishes for a fresh start. I'm sure they'll do fine.