I know it's been a while but I wanted to give an update on the situation. First of all, let me thank y'all for your awesome suggestions and help, especially KCW. You guys rock
The bike is running again as if nothing ever happened, and I didn't have to take it apart.
I should add that I'm not a complete beginner when it comes to working on bikes. I've been working on motorcycles and maintaining my own fleet for around 15 years now, and have had everything from a late 80s XJ600 with 4 incredibly hard to synchronize carbs to an XT600 and DR350 with as simple a carb as you can get to a brand-spanking new fuel-injected BMW R1200GS or XT600Z in my garage (the latter was surprisingly easy to work on by the way). However, in all my years I have never had to deal with a clogged or clotted carburetor even if I let the bike sit for 4 months at a time. And since I spent a huge part of my life in Northern Europe that happened pretty much every single year. The only thing I always made sure of was that the tank was full before I stored it for the long European winter.
Here's what I ultimately fixed my V-Star: first, I let the carbs run empty and took of the fuel tank and disconnected all the fuel lines to drain it completely. Running the pump with the lines disconnected helped as well, thanks KCW. Wouldn't have thought of that. I should also add that contrary to popular belief the fuel hadn't gone bad yet after sitting for a few months, as a friend's lawn mower bore witness to, so I put it in my car, added the rest of the Seafoam and filled the tank with fresh gas. The car ran perfectly fine with it.
Then, on a nice and warm day in January, I purchased Berryman B12 carb cleaner, added a bit to my fuel tank, filled it with fresh gas, and went for a ride in the somewhat hilly neighborhood. The engine was running as rough as before on the first few miles, but with each passing mile it got better and better, especially after following KCW's tip about going full throttle on uphill sections. The neighbors must've surely been annoyed by the lunatic going up and down that one hill over and over again
But it worked like a charm, and 30 miles later the system had improved to the point where the engine wasn't dying in idle anymore and ran almost perfect on low load and half throttle up to around 40 mph if I accelerated slowly. Full throttle and speeds above 40 mph still caused it to cut out, sputter, and eventually die after a few seconds. Unfortunately, I ran out of time (or rather out of Texas January sun...) and had to call it quits for the day, so I let the carbs run empty again and put it back in the garage.
Earlier this week I had an hour to spare again, plus the Texas state inspection was due, so I decided to take it out again. And to my shock and surprise it ran perfectly fine even on full throttle as if nothing had ever happened. Smooth, quiet, with no misfires whatsoever. The B12 must have worked its magic around fuel jets. After around 20-25 minutes I took it out of town and it eventually started sputtering again when doing around 60-65 mph or trying to accelerate full throttle, but it never died on me again. Three days later I took it to get inspected fully expecting it to cut out again at 55-60 mph but lo and behold: it runs perfectly fine now, accelerates without sputtering to 75 mph (couldn't go any faster around here) and does not cut out, sputter, or die randomly anymore. I've now done 70 miles since that first early January trip around the neighborhood and had no issues at all anymore.
Seems like I'm one of the lucky 10% that got away without disassembling the carburetor. I was ready to do so if the B12 hadn't done its job but it seems like I got away this time
Thanks again for your input and help, it was greatly appreciated. First time working on a new-to-me bike is always rough but I know I'll eventually get used to the V-Star and will be able to help others as well one day.