Ok
As the kit basically consists of a polish (PlastRX) and a buffer to attach to any drill my suggestion would be to use any "paint renovating polish" with a similar mop or electric polisher to give the clarity back to the headlight.
Provided the sanding has removed all the oxidised surface a good buffing will give the results you are looking for.
I found that spending the £19 for the kit was money well spent as the headlights are like new and there is still enough polish to redo the lights numerous times if the oxidisation returns.
The PlastRx polish costs less than £10 on it's own and is somewhat different to more traditional polishes see quote below
Meguiars PlastRX plastic cleaner and polish is a easy-to-use, rich gel formula quickly restores optical clarity to both rigid and flexible clear plastics. Cutting-edge advancements in Meguiar’s® exclusive Microscopic Diminishing Abrasive™ Technology (MDAT) remove light oxidation, chemical degradation, surface contamination, stains and light surface scratches with ease.
In addition, because the microscopic diminishing abrasives breakdown as you use them, Meguiars PlastX Clear Plastic Cleaner & Polish is safe on plastic rear windows on convertible tops, aircraft windows, motorcycle fairings, face shields, headlights and taillights, instrument panels, all clear plastic boat surfaces and aquariums.
Meguiar's PlastRX also contains highly water-resistant polymers. These specialized hi-tech polymers provide long lasting durable protection to keep your clear plastics clear and beautiful longer.
Good luck