It seems the ignition lock w/keys and the trunk lock is no issue in the parts system - but the seat locks have to be ordered from some place over the horizon.
A month is too long. (though, frankly - the hold-up on ordering parts was smack in the middle of my dealer parts counter. Once they got around to ordering the part it came in a few days - then they forgot to call me. Now I do my own ordering with quick service.)
The other good Taiwan scoot is the SYM....and people who own them tell me that getting parts was a nightmare - but now it's just difficult.
And if your Vespa dealer does not have the part in stock - they say it is best to lease another scoot while you wait for the Italians to stop cooking and arguing so they can look for the part and put it on a boat.
Can you photo the messed up seat lock when it is removed - so we can see what goes wrong with them.
All three locks were a problem?! Almost sounds like it was a bad key cut.
Stig