Long story short, Austin didn't even really need to "transition". We put him to bed in his bassinet and he slept just fine. We doesn't sleep 10+ hours anymore, but he still sleeps 8 and that's pretty good! Unfortunately, my little buddy is a BIG little buddy and he's already grown out of his bassinet so I cleaned up the old pack-n-play and Austin slept in his new big boy bed for the first time last night.
I'm still angry with Fisher Price because the motor is on back-order (which tells me the motor breaks frequently enough that they can't keep up with their product breaking down) and I won't be able to use the swing at all for a few more weeks, but their poor product was a blessing in disguise. It forced me to take Austin out of the swing and he's doing great in his big boy bed!