Evergreen is a perennial onion (a multiplier type) so should suit your purposes. There are a dozen or so varieties of Allium fistulosum available.

Are Egyptian Walking Onions a variety of Allium fistulosum? I ordered some on ebay.

I guess I'm not clear with what objective I have for these in my garden. Onion prices got high last year and I do not currently have great storage, so perhaps I was hoping for something to harvest other than on the usual onion cycle in my zone.

No , Walking onions are Allium x proliferum. If you want regular onions (Allium cepa) these are not suitable. In either case they are best used as green onions, altho the bulblets from a topsetting onion will keep for a good period of time. Not any bigger than pearl onions tho.
{{gwi:75377}}

Last year I direct-seeded a new-to-me onion from the Territorial winter catalog called Longkeeper, rated at 240 days. The seedlings were quite hardy, though I'd keep them under a tunnel next time to reduce soil heaving. Anyway, they bulbed up three weeks ago and we've been eating them fresh since they're the best onion we have right now. Our other onions have at least a month to go. We're at a transitional latitude (37dg), so I don't know how they might do elsewhere.

Generally the neck size is a good indicator of the size the onion will get once it bulbs. So I'd think you should have some nice sized onions.
As far as overwintering onions go there are many varieties available, mostly Japanese varieties. The ones that i'm about to harvest this week are Topkeeper, Desert sunrise (red), Highkeeper, T-420 and Bridger. You can find seeds from Osborne seeds, Johnnys, Territorial and some much larger companies like Logan Zenner and Bejo.
Keep in mind that overwintering onions won't grow without protection in areas that freeze hard on a regular basis. Here winter temps rarely drop below 15F.
good luck!

Thanks for the list, mad. The one I grew was Topkeeper, not Longkeeper. I wanted to try some similar varieties this fall and didn't know which varieties to look for.

I'm not too sure if an onion like Topkeeper would succeed in zone 5. It will be fun if the onion bulbs turn out in proportion to to the size of the plants this year.

Tim,
How do you start your onions from seed? I have tried the last two years and have had colossal failures both years and ended up ordering plants.

Normally we start tomatoes, peppers, broccoli and others and end up with some nice plants to set out, but the onions died out after sprouting both years. Something is obviously wrong. I'd like to correct so that we can grow onion varieties we want rather than just what is available as plants.

Wolverine, Onions aren't all that much different than the other things you start successfully. Keep experimenting, you will find what works for you. They grow slowly so it is a good idea to start them at least a month ahead of other things. I suspect that they need less bottom heat to germinate, but that doesn't sound like the problem you had. I don't transplant them after germination except into the garden. If they come up too thick, they still seem okay. They need trimmed back about once a week if they are growing right. When I transplant them into the garden, they always seem so small and fragile that I wonder if they will make it, but they always do. Every single year when transplanting I am thinking "start them earlier next year." I saw some pictures of onions growing from seed in a thread on one of the other forums on this site.

This is the thread I kept referring to when starting my onions this year. They're doing wonderfully!

Here is a link that might be useful: Onions from seed