I'm in Minneapolis and your description of your weather sounds a lot like ours here, except maybe we get less rain in the spring. I grew Inchelium Red for the first time this year and it came out great! I'll let others with more expertise suggest other variaties (plus, the other two garlics I grew were hardnecks and sounds like you're not interested in those.) Good luck. Very satifsying crop to grow. I am tripling the size of my garlic bed next year.
Sally

Thanks!

Yeah, I need garlic that'll last in the pantry, so no hardnecks. :)

Also now strongly considering Polish White!

Meeting all your requirements in a single garlic might be tough. The hardnecks usually have larger cloves than either the artichokes (Inchelium Red) or silverskins (Rose du Var) but they don't store as well. How long does "as long as possible" need to be? If you're content with a July harvest and seeing some sprouting around February / March, I'd recommend growing some hardnecks since they'll really perform well in Zone 5 and their taste is way better than store bought.

For hardneck varieties, that once well cured have stored on a shelf in the pantry until March for me, I'd go with Siberian (cloves between a nickel and quarter in size and hot tasting), Music (good size and easy to grow) or Polish Hardneck (stores the best with big cloves). I hear that Chesnok Red is also very good and easy to grow - I drowned mine the first time I tried it so I don't have real firsthand experience.

Another nice thing about hardnecks is if you let 1 form a capsule and go to maturity, you'd sacrifice bulb size but get a bunch of bulbils. Plant these either in fall or spring and use them as garlic scallions as they grow in early spring to tide you over until the main harvest. You can also chop and freeze a portion of your main garlic crop to have garlic in late winter and it will taste much much better than the chopped stuff you buy in jars.

For sellers, I've used Filaree, the Garlic Store and Seed Saver's Exchange, all with good results but order early ... the later you wait, the smaller bulbs you seem to get. Have fun, garlic's great to grow and it's really nice to see something green poking through the snow on a cold day.

9 months if possible. That way I'll have fresh garlic all year (the California early will be coming in as I run out). So really not looking at hardnecks.

The more I read the more the Polish (aka New York) white sounds like what I want.

Grow one of the hardnecks for first of season use and a soft neck for end of season use, of course, you won't like the softnecks as well after trying a good hardneck. BTB Martins Old Heirloom is reputed to be a good keeping hardneck.