Give it a little tap forward with some wood or something to see if you can reset the "O" ring that is leaking.
That happens allot when trying to get the valve cover in and out.
Dude......old machines have to be maintained.
In answer to your original question, the manual says to remove the carbs in order to get access to the thermostat housing assembly. I replaced my thermostat without removing the carbs, but I'm not sure which way would be easier and faster. If you remove the carbs you can probably get by without disconnecting the throttle cables - all you need to do is get them out of the way (slide them off the boots to the left) - and then work from the right side of the bike. To me, reconnecting the throttle cables is the worst part about removing/installing the carbs. WD-40 really helps get the carbs back over the boots.
Why remove the carbs? There's ***one*** screw that's a pain to turn, even with a 90 degree screwdriver. (It's not the only screw, just the only one that's a real pain.) The head of the screw is underneath and the carbs restrict movement to a few degrees. To me, it's one of those things where you grab a 7 year old for some "hands on" learning. Small hands, tight spaces, bad lighting, young eyes...
I'm sorry the bike is frustrating, but additional maintenance is the nature of everything with age, from bikes to cars to interstate highways to houses to the space shuttle and even, as I'm finding out at half a century, to people. I've had my '97 since day 1, and when something needs attention it's like a child trusting me to make things better. I've had cars that did not invoke that feeling, and they're all gone. The bike - she's my baby. My non-bike friends don't understand why I put in so much time, money, and effort on maintenance, but they all know how I feel about my bike, and they all say I seem almost as happy working on it as I do riding it.
Unless your a Connie carb guru I suggest sending your carbs out to be service by a guru. The words 'Clean the Carbs' means different things to non Connie Carb guru guys. Most people do not have the proper tools to service these carbs yet they will say the carbs have been (cough cough) 'cleaned', even some dealers too (but not all). Spraying carb cleaner in it is not going to get you cleaned, checked and properly serviced carbs.
If you were to watch Sunny Steve do a set you would know what I mean.
Also if you dont have over flow tubes installed have that done too please.
More than $300 to clean my carbs? No thanks. I've dumped more than enough money into this bike as it is. Might as well learn how to do it myself. A good soak in Pinesol, plus carb cleaner and wire through the jets etc should do the trick. As for tools, what special tools do you need to service carbs? A couple screwdrivers and pliers? Only thing I can think of is a carb synchronizer.
What kind of mileage are you getting? If it's 40+ and your idle is smooth then it may not be worth it during riding season. Most of us who are in the snowbelt do that stuff over the winter. (Of course, when I was in Phoenix, summer was the time to work on bikes and drive the air-conditioned truck - winter was awesome riding weather.) It takes me about 5 hours to clean the carbs and adjust the float levels. There's a write-up somewhere on cleaning the carbs, written by someone who owned/owns a zg1000. It is about 5 pages. You'd think there would be a sticky to it... If you want I can see if I have it on one of my home computers. Maybe someone else can post it first.
Here's the carb cleaning info plus a few good pics. I really don't know why this info isn't in a sticky. .....
I've got an 87 and in the last few years I've gained some insight for you.
First, you can replace that o-ring without taking carbs off. Come from below with a socket and extension and carefuly take the bolt out.
Second - this supercedes the first - If that o-ring is bad, which it probably is because it is hard and deformed, the rear coolant log o-rings (2ea) are probably bad too. Order a complete set from Murphs, comes with front engine log rings, rear log rings and thermostat rings.
Third - You will need to remove carbs to do the rear o-rings and the thermostat ring comes out at same time. When you have carbs off, getting the rings replaced is super easy, but drain your coolant first.
Fourth - You may as well replace the thermostat and thermostat cap oring at the same time because that ring will be toast if not prev. replaced.
Fifth - Order from Murph a set of o-rings for the carb connections. Order a set of bowl gaskets. Order new needle valves because once you're there and the bike is so old they may as well be replaced, order the air jet o-rings and little washers (4ea). Murph has all this stuff. Also order the Tygon fuel line to replace yours if yours is OEM because it is probably not too flexible anymore.