Well, it would be tight but you can certainly try to plant 6-10 seeds to see what happens. 65 days is just an average, there are far too many variables which will affect the actual harvest date. 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. 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. See how detailed this example is:

I have root pruned them even in late May here in Virginia so it should be no problem where you are.

I started seeds in a plastic covered hoop house (high tunnel) in late september through mid-October for a winter garden (direct sown in the soil) and then later put on floating row covers in zone 6 in Massachusetts without issue. I wish I started the plants earlier but I had plenty of greens for the winter. See my pic from late December attached. Assuming that you aren't further north than I am (ie with less light) you might be okay.

I would sure not count on killing this grass for this year planting, but start doing it right away by covering it with cardboard or anything else you can find. I used weed barrier - it worked fine, I just happened to have a roll in the house when I moved in. I am not sure about Southern NH, but here in Worcester, MA, about an hour drive form NH south border, soil is full of rocks. And under the grass it is probably a lot of them. In the beds, hopefully, they already gone. So I would count on growing in the beds, and the rest in containers. Lets see, what we can fit this year. Turnips - grow very fast, and germinate easily. Can be planted through out the summer. So plant as soon as you able. Cover with tulle - cabbage fly eats the roots in my area every year, if not covered. Carrots - germinate faster when it is warmer, but doesn't like summer heat, so choose one that grows fast. Actually,I wouldn't hold my breath for carrots this year. Beets - a little late, but will grow if you manage it to keep soil moist before it germinates. Radishes - I would say late, may bolt because of the day length, but you can try. Herbs - good time for planting dill, a little late for parsley from seeds, easier to buy plants. Lettuce - anytime Cabbage - OK for planting very fast growing, like "Golden Acre", or wait a bit and start in pots on the porch for a fall crop.I cover with tulle as well - works pretty good. Squash, zucchini, cucumbers, pumpkins, pepper, tomatoes, eggplants, melons(fast maturing) - good time for planting, wait until end of May(depending on the soil temp and weather), you will have to buy plants though.(I always start extra and offer them for my neighbors for free, so if you do not minds an hour(?) drive, I can share with you what I have. Shoot me an email, if you want to arrange something... ) Cucumbers has to be covered in my area due to cucumber beetle, so I grow only parthenocarpic ones in the vertical "greenhouse"-like setup with a net instead of film. Also powder mildew usually comes later in the season, so spray preventive (I use Serenade) to prolong season. Potato - OK to plant, but has a space concern - may be prepare for the next year. Or plant in bags. I found red pontiac very productive in our area. Do not plant near tomatoes - late blight always starting on potatoes first. Beans - perfect time to plant Corn - perfect time as well Onions - I would say too late for any type, but you can buy chive in pots and plant. Garlic - if you find any of last year(I may have some, if will not dry out completely), you can plant it for greens right away, and plant in October for next year. Sorrel - good time to start from seeds OK, I guess it is full list of veggies I currently grow)