Tixin, taking the carb off and taking it apart is really not as bad as it seems, it just takes a little bit of patience!
Honestly, I think the worst part of it is putting the carb back in place on the bike, that's the part that takes me the most time (about 5 minutes).
To drop the bowl, you'll need a phillips head screwdriver, it's 4 screws on the bottom of the carb. They can be tough to get to though, so patience! When removing the bowl, use a little caution as the float is in there as well, you may need to wiggle the bowl a little to get it past the battery box.
If you want to try squirting gas in the vac port on the right side of the carb first, then I would reconnect the hose before cranking. Or you could leave the hose off and set the petc0ck to prime. Bill means to set the petc0ck to prime and then crank it, I believe. The seafoam in the bowl won't go anywhere if it's not being forced through the carb.
In all honesty, it seems like your best bet would be to pull the carb off and clean it out good; it may seem intimidating, but it's much easier to do than it sounds.