I was the good buddy helping here, so very vested in this issue. I didn't touch the bottom end, only the top (hehehe).
1. Even though the kick wasn't touched could something "down the line" in the transmission affect it?
2. OR my second guess, could when Robert (thegoodlife) installed the clutch basket shifted something, causing something to block the kick (or are they two 100% different mechanisms?)
What's weird, like he said, is when you push the started button, it frees the kick?
Any help would be amazing, unfortuantely we do understand the worst case scenario is re-pulling the engine (actually theres always an even worse case, ha), but maybe, just maybe, its a clutch interference.