I had to remove mine. I removed the housing, a bracket that held some electrical connectors, and pulled the wiring harness up and out the right side of the frame. It was just enough to be able to force the surge tank out. I had to do a major scrubbing on mine. Look up in there while you have the carbs out. Might be dirtier than you think. When the rubbers get older, they let in more dirt than I like to think about.
As far as I know, to remove the carbs you just have to move the surge tank up a little to have enough room to get them out. Most people that remove the surge tank (air box) don't plan on reusing it. I think they cut it up or end up destroying it to get it out. If you plan on reusing it I've read that you have to remove the engine to get it out in one piece.
El Taco was able to get his surge tank out without destroying it. I believe that's a first. I'll be interested to see if he's able to get it back in as well.
But on the original question, I've had my carbs out 3 times in the last 2 weeks. I remove the bolt that holds the thermostat housing to the frame. That allows it to lift up when you lift the surge tank. But I didn't disconnect any hoses. Another thing I think saved me some time was that I disconnected the choke cable at the handlebars and then thread it through the frame - rather than disconnecting it at the carbs. The last time I disconnected the choke cable at the carbs, it took me awhile to get the cable reconnected. I only loosen the throttle cables - didn't disconnect them at either end.
As mentioned, lifting the surge tank in order to lift the carbs is essential to clearing the cylinder intake ports.
You can get the surge tank both in and out without total destruction, but it takes some patience and some isometric work. El Taco's idea of moving the wiring harness is the best idea yet; but basically, yeah, you have to pull everything else outta the way (incl the thermo housing, hoses (air and coolant). Then you've just gotta find the right angle, use some leverage, and work it over the cylinder head (note: removing the head cover does not make the reinstallation proces any easier...).
I can see why folks are going to canisters rather than keeping this filtration system on - even after you get the surge tank back on, you have to fight to get the ducts back in the tank, on the filter boxes, etc. But it can be done - just take your time.
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