I retired in 1991 so my knowledge of your engine's design and circuitry may not be up to date... but the following is worth mentioning.
Am I correct in assuming that when the engine is tilted up, it is also tilted to the left (Port) side? If so, anything dripping will naturally be on the port side of the engine.
Fuel dripping from the carburetors is a common problem, hence the need for good gaskets on the carburetor face plate assembly.... and also the hose on the port bottom rear side of the face plate assembly, a hose that leads to the bottom main bearing area. If this hose still exists on the 1997 model... Is it attached properly?
The gaskets mentioned above... are they in good condition and secured properly?
Some manuals give instructions in setting carburetor floats that I've found to be in error (my opinion)... The results of those settings leave something to be desired. I've found the following technique to be suitable for "all" horsepowers.
(Carburetor Float Setting)
(J. Reeves)
With the carburetor body held upside down, the float being viewed from the side, adjust the float so that the free end of the float (the end opposite the hinge pin) is ever so slightly higher (just ever so slightly off level) than the other end. And when viewed from the end, make sure it is not cocked.
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Should your fuel tank be higher (very unlikely) than the engine, a natural siphoning effect would exist, causing fuel to draw from the fuel tank and flow out of the carburetors due to the tilt of the engine causing the float setting to be non existent. Also.... when the engine is shut down, those carburetors are full of fuel and with the engine tilted, fuel is going to drip somewhat regardless of the tank's location (the reason for the gaskets and the hose mentioned above).
However, the description of your problem, to me, is to an extreme and suggests something out of the ordinary field of known encountered problems. I'd suggest you clean the engine up good, then have the hood off and the external carburetor face plate removed so that you can see the carburetor throats. Now, have the engine tilted as you would normally have it and scrutinize that unit for leakage.
Let us know what you find.