not much will carry over either due to fitment or appropiate sizing for the performance of the engine. what kind of TIV were you looking at? 2056 i believe.
carbs for the 2056 would be larger than you would want to use on the 1600, but you might be able to go oversized on the 1600 for now. ignition can carry over. and if you are going Cali conversion, you can reuse some of your cooling tin. nothing else is coming to mind. exhaust will not move over save maybe a muffler if you go with a TIV exhaust that uses the T1 flange (FAT, LAP, A-1 and some others). so you could get a PhatBoy or the likes.
my advice would be safe that money towards the TIV and live with the T1 as is. consider it motivation by de-motivation. you will find yourself saving money much quicker if you live with the pain of the stock engine.
another alternative would be to throw some money at a used 1915 or 1835 T1 for the meantime and then cherry pick the few things that can move over.