I have the same problem on almost every moped I ever get, and a few basic things are usually enough to solve the problem.
New carb? It's probably fine, but if you're so inclined, doing small things like setting the float level will probably help. Just general tuning crap. If you didn't get the stock carb (do they still make those? I have no idea) you might want to check and make sure the jet is the right size. I feel like when I bought a new carb for my hobbit I had to buy a clone, and the jet was way off... but I might be remembering wrong. Sounds like you could double check the idle setting, and the stock carbs have a mixture screw as well.
SET THE TIMING. I bet that's 90% of your problem. Check the points, clean them, etc.
I also clean the exhaust and port on broken mopeds. Do the BBQ thing, or I usually use a torch unless its really bad. Decarbonize the port, it's probably pretty bad.
A new spark plug wouldn't hurt, but I don't think it's causing your issues unless it's really bad.
On hobbits, I would check the variator. I doubt it's causing your problems, but can't hurt to make sure it's working right and maybe even tighten the belt. I tightened my variator on my hobbit and I got a few extra MPH
Lasty, I always check the compression and usually end up replacing the rings. If your compression is fine, then you're probably OK, but I could see bad rings causing those symptoms. Can't hurt to replace even with good compression, but if youre compression is good it's not causing your problems.
On hobbits, it's also worth it to check the decompression valve if youre compression is low. Might be stuck open or otherwise broken.
Also, I should point out, this is just a list of all the stuff I do with broken mopeds when they run like crap. On my hobbit, I had similar symptoms to you once because the exhaust was broken. Is your hobbit running kind of loud, like you can hear sharp pops? It should be more like a muffled growl sound. If it's really loud I would check your exhaust or decomp first.
Then, I would set the timing. Either way I would do this, actually.
I would do all of the things on this list, and then see if you're still running slow. All of this should take an afternoon, except the rings if you have to order them. Maybe one trip to autozone or napa for the plug, shouldn't be too hard.