The base question is why you're planning to tear into the motor in the first place. Once that's been answered, it'll direct the rest of the what should be done.
If the cost of an MJN22 carburetor is more than seems worth investing, then I'd focus on getting the motor as close to "mechanically new", ready for another 40,000 miles and optimizing the stock setup. Going to a 51mm bore just means using-up all the extra cylinder thickness and ending up with 4th OS. 113cc isn't going to make more power than the original 109cc. Power gains are really kinda underwhelming on the seat-of-the-pants-dyno, until displacement is around 140 and that's gonna need a bigger budget. There can be some decent hp gains but you won't really feel them below 50-55mph. From that speed up, the engine will just keep pulling, not leveling-off until the speedo reads 5-10mph higher than what you have. That kind of power could be made with the stock bore size...you'd need to raise compression and the rpm at which peak hp is reached, using a "hotter" cam. If your engine is making full power, you should be seeing low 60s (~100kmh) on the flat and be able to sustain 50-55mph, closer to 60 under ideal conditions.
A head rebuild is pretty basic on this motor, the parts are inexpensive. They're also durable. I've not seen one of these heads with wasted valve seats. At most, a light cut, new valves + lapping was all that was needed. As long as the casting itself is sound, there's not $100 total in valvetrain parts. With the head removed, you have to decide whether the piston has to leave the bore. If there's no oil control problem and no scoring, then it's your call as whether you want to gamble that all of the lower end parts are in tiptop condition.
Once the piston leaves the bore, you'll need to deglaze the cylinder and buy new rings, at the minimum. At that point, it'd be pennywise and pound foolish to not split the cases and inspect the lower end. On one hand, the lower end may need nothing. You spent an afternoon cleaning and end up with cheap peace-of-mind. Barring any surprises, I doubt you'd need to replace $150-350 worth of lower end parts...giving you a lower end that is literally good as new. It's still cheap peace-of-mind. A new motor is 2500EUR + shipping.
The lone modification that might be worthwhile is some light port cleanup. Concentrate on the exhaust port...removing casting flash and working on the short-turn side of the port, to give more of a straight-shot from the vale to the port outlet. Keep the material removal to a minimum. Hogging-out a port, substantially increasing its volume, will kill flow velocity and result in soggy lower-to-mid range scavenging & performance. On the intake side, you just want to remove any casting flash; leave the port walls rough. The exhaust side, OTOH, can be polished if you like; that's not really worth the effort.