If the bike runs on choke but dies, the pilot circuit is clogged. Either the internal passageways or pilot jets. The choke circuit is supplying a bit of gas to keep the bike running but once off choke, there is no gas. It is also possible you are not warming the bike sufficiently for the bike to be taken off choke. I have a set of GPz750 BS34 carbs on my GS1000G and those carbs are similar but jetted differently than yours but they are VERY VERY lean when cold and need to be left on choke for quite awhile before I can drive off and even then must use partial choke until the bike is fully warm. I used the GPz carbs rather than the GS carbs looking for a bit better gas mileage. they get about 4-5 mpg better but as noted, are cold blooded. If you find that you can't warm the bike and then take the choke off (showing a bit of patience), the pilot circuit likely needs cleaned out and/or new pilot jets installed.
Texas Hill Country