Well, if your sail has a boom/clew length of 220 cm and you only have a 222 cm boom, you may have a bit of a problem.
The stated boom length on most sails is the median length required.
If you want the sail more fat and juicy (more draft) then you can simply not outhaul the sail as much (back off on the downhaul a bit as well so the top does not loosen up quite so much) and you will have an OK boom length with your 222 cm.
For median, if your Tush Lightning needs only 220 cm then you would be OK there as well with normal downhaul, but it leaves you with almost nothing if the wind comes up and you want to flatten your rig a bit.
Where you will really have the problem is when the wind is up (for this sail) and you want to add additional downhaul to get more top twist and flatten the mid level panels a bit more.
Anytime you downhaul more, you bend the mast more, and this causes the required clew length to increase (quite a bit on some sails).
Now you have the problem of a longer clew length and no way to extend your boom.
Also, booms all tend to be a bit more bendy and flimsy when extended to the max. possible. This is due to a very minimal tube overlap ( outer main tube over lapping the inner tail extension tube.
I like to stay at least 10 cm longer than what the sail requires (in your case that would mean a boom length of 230 cm min.) plus a little bit more tube overlap simply gives you a stronger boom with a mre solid feel.
As far as getting planing on your Carve 145 with the 7.8 m2 Tush Lightning, I think you will be planing pretty easily in a solid 14 knots and with some pumping and heading offwind to get up to speed, you might get going in 12 knots at your weight.
It will depend on your technique and how you rig the 7.8 m2 Tush.
Make it fat juicy and drafty and you can expect quite a bit of low wind power.
Rig your sail more lean and fast and you won't get going so early (or as easily) but you will be able to handle significantly more wind.
Boston in September should be quite good.
There are some places to sail right near Boston, but I'm not sure about renting gear there.
Most of the shops that used to be in Boston have moved down into the Narragansett Bay area or out on Cape Cod.
You will be fairly near the shops when you are in Hyannis, and there's a great sailing area just down the road.
So, when you pick a rental car, get an SUV or something with racks, drive out to the WS shops near Bourne and Falmouth, rent your gear and go sailing.
Here are a couple of links to shops I know in that area:
If you decide to make a side trip to the South, come down to Cape Hatteras and look me up!
Hope this helps,