I'm guessing that the 'ride' is better on a newer Vespa than it is on a newer LIKE200i.
'Shakes' may not
all be down to the tires?
Because I was going to use my new 2013 LIKE200iLX for 365 work commuting in Ohio - at @450 miles I paid the dealer to swap out the Kendas for a set of Michelin City Grips. Tires and installation was @$245.
They lasted for years, and performed well in all types of weather.
Some balance beads into your Kendas might rid them of the shakes? (they go in through the tire-valve stem)
If you are not a "sporty" rider who loves to scrape things and run your LIKE at top speed - and do not ride in the wet - the Kendas are probably A-OK.....but you won't be disappointed with a set of Michelins either
Stig