I am using the choke to start. Excuse my ignorance, but if an orifice was clogged on the carb, would it even start?
There is more than one fuel circuit in the carb. At or above part throttle the main and slide needle meter fuel, especially with the choke applied. This allows the engine run until the throttle returns to idle position. It’s possible not all the pilot jets are clogged. That’s why I told you to check the exhaust headers for temp. Clear pilots will allow the head pipes to heat more. Then you only have to clear the carbs related to the colder head pipes.
I would also verify that each of the four float bowls are filling. I have seen float valves get stuck from sitting, too, which will stop an individual carb from working entirely. Again a cold exhaust header would tell you which corresponding carb is at issue.
You can flash touch a hot header very very briefly. Your hand’s heat sensors are slow to react. But, have a bit of memory to relay relative heat after the touch. Only repeat touch when you are certain the heat is low enough not to burn. You can think of it as a digital sampling technique. Very short contact events you repeat as needed to get a heat sense. Assume the next pipe is too hot to hold, even if you initially find a cold pipe You can hold. Or use one of those cheap temp guns from Harbor Freight.
On some occasions refilling the bowls with fuel can dissolve dried gas deposits. This is a welcome “self cure” When you are lucky to encounter it. But, if the blockage remains after few days of soaking, more invasive action is indicated. You don’t have to remove the carbs to access the blocked components. Just the float bowls and a bit of human contortions.