You can try to trick them into bulbing a little bit more by breaking off the flower stalk but they probably won't get too much bigger. You can still use them though, just use them first because they won't keep very well.

As far as planting a second set goes: you can plant them but they are daylight triggered to initiate bulbing (length of days). It depends on whether it's a short day or long day variety.

If it's a long day variety because we're so close to the solstice, they'll probably never receive that trigger since days will be shortening by the time they're established so likely wouldn't initiate a bulb.

If it's a short day variety AND you get lucky, they'll establish before the length of days drop below they're threshold and they'll start to bulb. The resulting bulbs are likely to be small though.

Now, that said there is another option.. you can plant them and grow them intending to use them as green onions/scallions.

Good advice above.

My suggestion as a long term Oregonian is next year, don't plant sets, plant starts. Starts are little plants that look like mini scallions. You can grow them yourself or find them at nurseries in the spring.
Onion sets are way too prone to bolting just the way yours did.
Sorry you found out the hard way....

-Mark

I do have a heat mat and light to start my own from seed for next season, when would I start them, sometime in the winter i'm assuming? Is it worth it to try overwintering them or will I run into the same problem with them bolting?

Onions that will overwinter and bulb in the spring are very specific varieties. I think if you use those sets again, i'd expect more bolted green onions (which are fine for lots of things).

I start my onions the first week of Feb in my greenhouse with no lights. There are lots of posts on this forum with tons of details on how to use lights and heat mats inside if that's your best option.

-Mark