[Jacob Bendicksen]

As you probably know (I've seen your robot at the event!), we host BunnyBots, and that's how we train our new members. We try to have the rookies do the bulk of the robot-intensive work and have veteran members take on more of a leadership role (and less of a hands-on one), and that's worked well for us for the past 6 years.

To address each of your possibilities:
Swerve: I know 2471 did an awesome swerve this year at BunnyBots, and they're using it on their current competition bot. That seemed to be a great platform to test the swerve.
Training new members: BunnyBots seems to do this well, but smaller projects can be good, as well. Small Arduino-based projects can be a good way to get used to building physical things alongside an easier programming environment.
Team bonding: try to have semi-regular meetings during the offseason (monthly at the very least). I'd imagine that you get together at some point to build your BunnyBot, so try to have most people show up to those build sessions.