Perennials: Salvia with mealy bugs, 1 by 3gardeners

3gardeners wrote:
I'm new to Salvia and to top it off this is the first time I have EVER had mealy bugs. I noticed them on my black and blue, 3.5 foot tall salvia, but did nothing at first because I was busy, forgot about it, didn't think much about it.... Anyway, I went back to that part of my garden a couple weeks later and the salvia was dead looking on the branches (half of them at least) with the bugs AND they were spreading to sages and lavenders and across the ground from one plant to another.
I did lots of reaseach and came to the conclusion they were mealy bugs (although, I didn't see any of them crawling). I sprayed with insectisidal soap, nothing, ~ week later I used some pesticide I had in the garage that said it killed meally bugs. They stopped spreading , but there was no difference in the way they looked. Just white up and down stalks. I cut the dead parts of the plants off.
Now we are finally getting winter weather, and the remaining dead salvia stalks are still there with this white stuff all over them.
Question: Since the season is over, I was planning on cutting back the salvias and sages and other dormant plants now.
What can I do to encourage these plants to rebuild their strength and return next year?
Or are they most probably already dead?
Should I dig them out and sacrafice possibly live plants to erradicate the bugs?

The white stuff seems to just sits there and stare me, and I just stare back because I don't know what to do.

Any help would be appreciated. Thanks!

(this photo was taken this summer)