@pedrazo welcome here within this hive!
For my next steps I was planning to
1) pull the spark plug to see if it cranks without the hesitation and
2) open up the kickstarter to see if something is engaging there. But do you all have any other thoughts? I'm even less electrically-inclined than I am mechanically-inclined but have now had this bike apart more times than I can count trying to figure this one out. Thank you!
To 1: good idea to check how your motor cranks without plugs
To 2: if the kickstart would be engaged, there would be a rattling/ grinding noise to be heard.
BUT, to eliminate this as a culprit take off your CVT cover and have a look into.
Try to start without it, let's see.
Go direct with small jump cables from an external battery direct on your starters plus and minus. How is it behaving?
Try to put an additional cable from battery minus to your starters minus/ ground. Dielectric grease helps only when the ground parts are mechanically clean/ blank and not corroded.
Also within one of your power cables might be corrosion, therefore direct.
Pls see this link, maybe some idea comes up.
https://www.kymcoforum.com/index.php?topic=31637.0With starter solenoid you mean this relais on the scoots upper frame with a fat red and black cable?
If this clicks only, then too less energy is coming even a new battery is installed. Cables corroded or not tightly fixed.
Pls give us a feedback to learn.