im starting to hate my tw

ive done almost everything now. new carb parts 117.5 main jet. new needle and seat. carb is 100% clean. i am pretty sure it is the cdi unit. it runs rough and sputtery, almost like a lean issue, but i know it is not because i have a brand new spark plug in it and it has black on it because ive been trying to fatten the hell out of it. it backfires when let off the throttle. im not sure anymore here!? the engine is sound. it have better than factory compression and the valves looked amazing. ive been chasing my problem as a carb issue but i think im going to have to go the more expensive route with a cdi. any suggestions on where to get one for cheap and fast, how to test for it. etc? it is a 1987