It’s tricky.
There’s no boot available that’s larger and has the carb face intake impulse entry. The stock 361 boot has an entry the same size as the 1128 boot, but it chokes down by the outlet. Some swear you can get by with the stock 361 boot, but I’ve always gone 1128 on a hot 361. Then you need the outer metal surround from an 1128 for the boot.
You’ll need an 029/039 impulse line. It’s long enough and there is already a hole in the stock tank for it.
As for the carb, it’s a pita. You need the choke shaft from the 361. You need to file the flat part open to accept the larger 1128 choke butterfly. The throttle shaft stays the same. The metering cover needs to be swapped out.
Then the stock linkage won’t work, because the now bottom/pump plate impulse elbow will be in the way. You have to make your own. Apparently a stock 1128 linkage flipped the other way works well, but I’ve always made my own with tig filler wire.
It’s a lot of work, but seems worth it. I’d love to compare a 361 booted 361 to the 044 boot with no other changes.