because his new bike feels extremely wobbly and top heavy during parking lot maneuvers
Nothing to do with the bike I'm afraid. Although different bikes have different characteristics, none of the road bikes you can buy from a dealer will have any nasty handling traits otherwise the lawyers would be all over the manufacturers like a rash!
This is very much a problem with the rider's abilities and is extremely common, hence all the 'duck walking' you see.
Would love to have ten minutes on a parking lot with this poor chap so I could fix his problems forever!
Dedicated to the wonderful sport of Moto Gymkhana