Andy,
It sounds as if the final drive shock absorber is riding over the top. With the spring and retaining plate removed, turn the sprocket to see how far the cam lifts - it should lift higher than the end of the centre sleeve. If it does, all is OK. If not, you may need to fit a thin spacer over the sleeve so that the combined height exceeds that of the sleeve. You should then have a large dia spacer (same dia as the boss on the cam) x about 1/2" thick, then the spring retaining plate. The 1/2" dia bolt that goes right through the final drive shaft should then be done up tight, and a split pin fitted.
The reason you may need to fit the thin spacer is that Mr Douglas changed the length of the sleeve at some point during the production run, and you may have a mismatch of cam and sleeve.
Don't worry about the backlash in 1st gear - this is normal, it makes gear selection a bit easier on engine speed gearboxes. If you turn the input shaft as you try to select other gears, it should change easily.
Hope this helps,
Regards,
Eddie.