Mtnboomer
Crowing
Im in the mtns of VA (heavy clay and rock). Our last frost threat is in mid may. I plant potatoes in march because potatoes tolerate frost/snow well. The leaves will die back but they rebound quickly. By the time july and especially aug gets here, they are finished growing and ready for harvest to avoid the heat.May is the best time to plant! You aren't too late!
Here in Utah EVERYONE plants in May because we always have a late frost right up until the last day of April! This is basically permanently like this, every year. Even now we still have snow on the tops of the mountains (but not in the valleys, and valley floors). Last year we had snow on the mountain tops until almost July; but that's a weird exception, its usually gone by then.
People in the Midwest sometimes plant later also when they are in flood watches.
You should be OK planting pretty much right up until end of May. Especially with potatoes because they are a root vegetable which weathers the sun better when the heat gets pretty intense.
You can probably plant other things besides potatoes even with this same cycle. But if you have seedlings coming up in the ground when you get that awful July heat sometimes you have to be creative with keeping them alive. But for potatoes you won't have to worry about that.
Over here we can plant most things, however, anything that takes up to 120 days or 110 days we have a hard time with here and it can be cutting it close. People do get corn to work here just fine. But for some reason I had a lot of trouble with sweet potatoes. I grew and planted sweet potato slips and the combination of needing tons of growing degree days, and low soil fertility (clay soil), etc we didn't do well. I would probably hypothesize you could probably avoid some of the vegetables that use huge numbers of days like sweet potatoes when you are planting later, and just plant the other stuff that you know will finish in time. But even then you can go with what the locals in your area can give you more specific data on. (Sweet potatoes are ~120 days).
Last year, we didn't get a measurable rainfall in 3 months and temps routinely hit mid 90s and higher. My father planted his potatoes late and water bans prevented irrigation. They burnt to a crisp and died by 1st wk of August. The potatoes themselves were fine but were 1/2 the size of mine.
Sweet potatoes are extremely frost sensitive so can not be planted until after last frost.