As of 2021 that Shimano 600 Group set could make you enough money to pay for at least half of what it would take to go to Brifters. You can spread the rear drop outs to take a 7 Speeds. You can find 7 Speed group sets still. So what you are looking for is a 7 Speed Indexed Group Set. You will find that more likely from an old Mountain Bike. That means the set will likely be a little beat up at best. I personally would stay with the set you have now. You should be able to go to a 6 Speed Free Wheel easy. You can get a free wheel with a 34T bail out gear. If your Shimano 600 rear derailuer is not long cage you can convert it pretty easy with long cage swing arms. You can also make some modifications to your crank. That will give you a wider range of chain to pull.
Oddly when it comes to old bikes Friction Shifters like loose balls rule!!!
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No matter where you're at... There you are... Δf:=f(1/2)-f(-1/2)