Riding the clutch at parking lot speeds with the Empulse is definitely not necessary, because a.) the bike can't stall, and b.) the throttle is so direct and sensitive.
In my opinion, low-speed maneuvering is probably the most difficult part of riding a motorcycle, period. Once you get up to speed, physics does a pretty good job of keeping you and the bike upright, but wobbling around at 2 miles an hour is a VERY hard thing to do, especially just starting out. The one downside of the Empulse vs the 250s you rode at the MSF is that the Empulse weighs much more (probably at least 100 pounds more) -- part of what you are feeling is the additional weight constantly trying to fall over. The throttle, though, is a massive win. As your wrist gets more sensitive and you get better at make those constant fine-tune adjustments to the throttle, you'll forget about the weight.
Maneuvering a gas bike at low speeds is even more difficult, because you have to worry about riding the clutch and stalling and doing something with your left arm in general. With the Empulse you mainly just have to be concerned with adjusting a giant light switch dimmer, effectively.
What I would practice (i.e. it helped me a lot early days) is balancing at stops. I actually still do play the game of when I'm coming up to a stoplight in traffic or whatever, trying to not put my feet down. Instead of coming to a full stop, try to inch forward as slowly as possible with your feet up until the light turns. It's a dumb thing that passes the time in traffic, but also helps familiarize your body with the balance of the bike and how various minute adjustments to throttle affect it.
Also I'd highly recommend casually farting around in an empty parking lot as a means of low-speed practice. If you have friends with bikes it can be a fun joint exercise as well.