Sounds like that Weber conversion is working OK! Is it the progressive-linkage 2-barrel that works like half a 4-barrel? I've worked with them a long time ago, but nothing recently. It seems it might be a little small for an engine close to 4 liters in displacement, if you're doing much high-speed operation.
Here's a suggestion for another approach. We're required to run a carb on the round track with no more than 350 CFM airflow, and Holley makes one for this application. It's a 2-barrel like the Blue Oval V-8's ran in the 60's and 70's, with smaller venturis and throttle plates. The Holley List # is 7448. JEGS sells them, in either manual or automatic-choke versions, I believe, and it will take a Chevy 350 to 6,000 RPM or so before it starts to strangle off the airflow. With a little adapting, it would be ideal for a hi-rev 292, and wouldn't over-carburate a 235 or 250. There are lots of jets, power valves, and other parts to tailor the mixture to your particular application.
Jerry