[drolston]

On a hot engine, it should take no choke to restart. Check the float levels; easy on your 97 carbs. Just after shutting down (on level ground), take the top off of both carbs (be careful with the accelerator pump plungers). The fuel level in both carbs should be about 1/2" below the rim of the float bowl.
If one is low, it might have a float valve that is sticking closed. The fix is to disconnect the fuel line to that carb and blast some carb cleaner into the fitting on the carb. If the problem comes back, replace the float valve.
To check the float levels, take some fuel out of both float bowls. With the ignition off, crank the engine and observe the float bowls fill until the float valves closes. Check the level at very close to 1/2" from the rim. If high or low, adjust; being very careful of how you bend the tab on the float especially if you have nitrile (plastic) floats. If you put bending pressure at the point where the tab attaches to the float, you can break the airtight seal of the float, which will sink and cause bad fuel overflow.

If this does not take care of your problem, report back for the next suggestion.