You seem to imply that you have grown Snap Peas before. How long into summer do you get productivity? In Ohio, I've grown Super Sugar Snap many times, and the plants just turn brown and die rather quickly by July. Got about 46 days until July 1st. So that would mean that they would not start producing peas until like 2 weeks after summer starts, so it doesn't sound good. maybe you would have better luck. You can buy plants if you can find them. Even Lowe's (in my area at least) has Bonnie brand pea plants, 'Sugar Ann' I think. Hardly an ideal situation, but you might get some snap peas to eat that way.

I am also in zone 6b. I will be planting my snow peas this weekend. Good luck to you! Peas are pretty frost hardy, so you can try them a little early and take your chances. If you succession plant (every 2 weeks plant a few, for example) you might be able to find the optimum time for your garden. Experiment and have fun. Most of the time there are far too many seeds in the packets for me, so you can lose a few without worrying about losing your harvest.

Check with your state's Extension Service. Each county should have it's own Cooperative Extension Office which provides free publications and information for the asking. They will have valuable vegetable/gardening tables available specifically for your area determined by universities, and horticultural research scientists who have collected data from growing those crops in your state. Your tax dollars are already paying for this service so you may as well get some use out of it. See how detailed these examples are: Vegetable Planting and Planning Calendar for Missouri (download the pdf) complete with spring and fall planting dates (underneath the spring planting dates for appropriate crops), how much to plant per person, etc. They can also tell you the average last frost date for your area and ideal planting times for specific crops and varieties in your area. Here is an excerpt:

Ditto on Denninmi's comments. "Plant as soon as soil can be worked" is not always practical, nor does that necessarily mean 'early'. For me, unless I want to plant in mud, that usually means sometime in May, or even early June some years. I can usually get away with planting shelling peas late, and often do... they still do OK here planted late. You might still be able to get in a crop of an early variety. Snow peas, though, are another matter. They are pretty much out of the question this late; the pods will be small & tough if they develop in the heat, and the plants won't make it until Fall. Sugar snaps might do OK for awhile, but PM will generally do them in during the dog days. Snap peas have done particularly well for me planted in July. My favorite variety, "Sugar Lace", actually does better planted for Fall... I get better germination, and the pods are sweeter when they develop in cool weather. I got lucky this year; just saw the weather graphic & my part of the state is in a 'sweet spot' that has only had 30% of our normal May rainfall (and less than that locally). My heavy soil dried out early, so I was able to till early, and got most of my peas in on time. I just planted a few varieties for soup this week, though; soup peas are not as finicky about heat.