If I were you, I wouldn´t give this starter issue (which isn´t really an issue by the way) too much attention.
My Like 200i has and always had the same "issue" for 4 years now since new. I also changed the battery but the "issue" remained.
I guess the reason for it is that the starter motor is a bit too weak for the engine in some cases when the piston is in compression stroke to start and turn over. At least at the second attempt the scooter always starts immediately.
See it positively that your engine (piston/cylinder) has a good, strong and healthy compression ratio.
By the way, the much more expensive Vespa scooters do have similar issues with starter motors. An observation I repeatedly made on my brothers Vespa GTS 300.
The TPS could be resetted also for a first attempt. Therefore the pink wire in the battery compartment needs to be put against ground (green) for a few seconds while ignition key is on.
Repositioning of the TPS afterwards is done by just 3 cycles key on and off for each a few seconds (I guess 3 or 5 seconds after each turn).
There is also a blinking code reset procedure available, but it´s more tricky to achieve propperly. I guess an instruction is already available here in the forum.
And as a general hint: Do not manually try to set the TPS unit by turning any skrews there!!! You will ruin it. It´s all factory preset and every possible adjustment needed afterwards can only be done electronically by the diagnostic tool from kymco!!!
Depending of which weights/rolls you are using there might be also a little issue in the drivetrain. If you are using the specially designed sliding rolls from Dr. Pulley you or your mechanic should have made sure that the variomatic plate edges were filed/polished down a bit. Otherwise the sharp edges could make the sliding rolls flip over and at least wear more rapidly and cause troubles also. If you want to know more about this, go to the Dr. Pulley website and read the blog there.
And your gas tank ventilation issues also have been discussed here many times already I guess - as far as I can remember.
The whole gas tank ventilation system is more complicated in the US than everywhere else on this planet.
And Stig for example is a very active and experienced member and administrator in this forum for the Like 200i. He has written many excellent point by point service guides with pictures - almost essays.
He knows a lot, if not almost everything.
Just try to read a bit in this forum - you will find tons of good and helpful stuff here.