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Lilac's can be pruned quite heavily. I would wait until early spring to do this.
Here is a link that will help you.

https://www.gardeningknowhow.com/ornamental/shrubs/lilac/pruning-lilac-bushes-when-to-trim-lilac-bushes.htm

Depending on the variety, dwarf lilacs planted in the ground are winter hardy down to zone 3 or 4. However, as you've mentioned, plants in pots are more exposed and sensitive to cold weather and will need protection. I think you could overwinter them in pots by wrapping them up (especially the pots) with multiple layers of newspaper, burlap, or other materials, with perhaps a layer of thicker material around the outside, and/or moving them into a garage or a spot protected from the wind. Here are some other techniques you could try:

http://lancaster.unl.edu/hort/articles/2004/pottedtreesshrubs.shtml
https://www.gardeningknowhow.com/special/containers/overwintering-container-plants.htm
https://www.gardeningknowhow.com/garden-how-to/mulch/mulching-plants-in-winter.htm

Severe pruning, or rejuvenation pruning, typically works well to bring old lilacs back. Your plan is generally good, but the best time to do this is thought to be in winter and early spring when the plant is dormant. However, less drastic pruning in the fall is fine too.

See these articles about it:
http://lancaster.unl.edu/hort/articles/2005/prunelilacs.shtml

There can be several reasons why a Lilac isn't blooming and the article below will help you pinpoint the cause.

https://www.gardeningknowhow.com/ornamental/shrubs/lilac/lilac-bush-not-blooming.htm

They may benefit from protection during their first winter. You could wrap them in burlap and mulch over the roots. Also see this article:

https://www.gardeningknowhow.com/ornamental/shrubs/lilac/winterizing-lilac-shrubs.htm

Most lilacs bloom in May or later, but there are some lilac varieties that bloom earlier, like Early Lilac (Syringa oblata), Syringa x diversifolia, and Chinese Lilac (Syringa rothomagensis). If you can find a source of these, you might be able to have lilacs in late April.

Most lilacs need cold weather, so Southern growers probably won't have them. Good luck!