You might consider keeping your Invader as a 340. There is certainly nothing wrong with those sleds, as several owners on here can attest.
I took a quick peek at some very common suppliers to the industry...and you are right in saying that the parts availability for the 340 is more scarce than the 440.
As gixxer mentioned, you can find some good replacement cylinders.
Are your cylinder heads in good shape? I would be surprised if 1 or both aren't still OK....even if not, you can get those from us on here.
You would just have to find a couple pistons, then...again, folks on here can help.
Keeping it as a 340 would eliminate the hassle of finding different carbs, different clutch weights, different gears, etc....and allow you to save your hard earned money to devote to new crank seals, new fuel lines and filter, etc. etc.