Rachel, I hear you loud and clear. I live in Lakeview (with no car) and I don't care much for the produce at Jewel or the Whole Paycheck on Halsted, but the one at Belmont & Ashland isn't bad.
If you can bribe a friend who has wheels with a home-cooked meal and I can almost guarantee they'll road-trip you to HMart. It is absolutely worth the trek, but I find their fruit needs tends to be a bit more ripe that I prefer. Their veggies are great and the selection of hot peppers, fish, grains, and meats is insane. I would avoid weekends if you wish to keep your sanity.
If you head out there with some other folks, you could in theory split the cost of an iGo (I've done that too). It's around 12mi one way Lakeview to HMart.