Finally a positive update on this situation (pardon the delay, took a while to finally resolve this)...
After replacing the carburetor and intake manifold, as well as all hoses and pretty much everything related to the fuel intake (at the recommendation of a few local Vespa mechanics), and testing the coil and battery as well (both were fine), the problem with the engine bogging persisted - and still the same problem when I used the turn signal/horn. It idled fine at start-up, but often it just wouldn't accelerate, other times it would accelerate, but then randomly stop accelerating in mid-ride - which is a recipe for an early grave if you're riding in Miami like I am

. At this point, I'd done everything I could to fix the problem to the best of my ability and the local Vespa mechanic had run out of ideas of what the problem could be, and thought maybe the valves might need to be adjusted (which of course, would be a pricey fix).
So, seeing no other options, yesterday I bit the bullet and took it to the mechanic to check the valves. After multiple attempts, I was able to get it accelerating, but about 1/4 of the way to the mechanic, it just shut down and wouldn't restart. So I pulled over and sat for a moment to ponder the meaning of life. When I finished pondering, I went to restart it and noticed that unless I turned the key all the way to the right and held it, the engine wouldn't turn over. Ok... strange, but noted. So I pull back onto the road and proceed to ride over some bumpy train tracks and the engine starts bogging again and, rather than pull over, intuition told me to turn the key all the way to the right and hold it again... and, surprisingly, as I did this the acceleration kicked back in and I was able to eventually make it to the mechanic (riding one-handed... all while holding the key

).
So after 4 months of trying nearly everything... and dropping an unnecessary $300+ and basically rebuilding the entire engine, it ended up being a bad ignition switch that caused all of those other issues lol. Literally a $17 part (the mechanic was a stand-up guy and just charged me for the part - no extra for labor since it only took him 10 minutes to fix). He admitted that he probably never would have figured out the problem if I hadn't made that discovery on the way there.
Since I have never seen this specific issue on any other posts/forums, I hope this helps somebody else going through the same problem.
Thank you all for your input!