Check the valve clearance, a valve not seating fully would make it "backfire". Usually a leaky intake will cause it too pop through the carb, exhaust leaking pops through muffler. As for timing and spark issues, just go to the nearest lawn mower shop and get a little single cylinder points conversion module. Can't think of the name of it right now, but they're only about $15. Usually you can get those little 70's running well for cheap. I'd try that before swapping engines.
'74 ATC70 (stock for my nieces)
'84 ATC70 big carb, race cam, and piped (big boys little toy)
'84 ATC125M
'85 ATC125M
'85 ATC185S (200X carb and pipe)
'83 ATC200X (my first trike ever, avatar pic)
'85 ATC200x
'85.5 Tri-Z 250
'85 ATC250R
'79 CJ7 w/351 Cleveland
'77 XL75, '78 XL125
'88 Katana 1100
'00 King quad
'05 LTZ400