I mostly agree with all of the above; except that I wouldn't even consider rebushing the carbs at this point. Just change the jet seals (Moss has some O-ring replacements for the cork that work <span style="font-weight: bold">much</span> better in my experience) and the float bowl gaskets (which never last more than 2 or 3 years for me). You'll need to recenter the jets and readjust the mixture afterwards, but those are basic skills that any TR3 owner needs to know. And not difficult at all, once you know how. For a first time, it's probably worth removing the carbs from the engine just so you can see better what is going on. But both operations can be done fairly easily with the carbs still mounted on the engine.
To check for leaking carb seals, touch your finger to the bolt that holds the float bowl; and to the bottom of the jet (clevis for the choke lever). If your finger smells of gasoline, the seals are leaking. They almost always start out not leaking enough to drip, just enough to stink.
Moseso's comment about the fuel tank is on the nose, too. Real easy for a pinhole leak in the bottom to go overlooked, except for the smell.
Oh, and you might want to consider some better ventilation for the garage :laugh:
I installed one of those "power attic vent" fans so it runs whenever the garage light is on and the air is above 75F, which greatly reduced complaints from SWMBO.