RE: engine cuts on landing approach...
Switch,
this may be very basic, but does your carb baffle have a small opening at idle? It used to be recommended practice to set up the engine so that it cuts at idle. In older days before computer radios, this was required to allow you to cut the engine in case of emergency and though modern competer radios have the "throttle kill switch", many instructors still setup in the older style. It could also be that the hole is too small to sustain ignition at idle, so just use End Point Adjust and open it a bit just a bit further if that is the case.
If all of the above is OK, it is probably a LSN problem. Engines gain RPM in the air (I learnt this the hard way when my kill switch did not work) so dead sticking in landing is uncommon if the idle is OK in the ground
Ameyam