Slack at the clutch lever is normal, and as it happens, necessary, I'd start by putting the play at the lever back how it was.
Motorcycle sequential gearboxes can be temperamental, even Suzuki ones, especially when new.. When this sort if thing happens just spin the clutch a little by letting the lever out to where it bites to disengage the clutch momentarily and then pull it back in and make your selection.. Over the years we get used to this and so sometimes hardly even notice it's happening..
The grease thing you mention is a linkage problem, where the unions in the linkage between the gear lever and the selector shaft, (the rod that goes into the gearbox) can dry up causing selection problems.. A strip and grease will sort that out.. I wouldn't have though it would be that on a 500 mile bike though..