Poor idle and off-idle performance after distributor swap

Ok gotcha!

A 600, on a 360 is IMO, still too small.
I have run everything from a 500 to a big TQ ( carter-rated 850), and my favorite is the 750DP.
I'm no fan of vacuum secondaries.
On my 367-combo, the 750DP is not too big. I have a clutch and a 10.97 starter gear.
With an automatic and handicapped by stall or gears, yeah a 750 might lose some low-rpm tractability, but as soon as you correct that handicap, away it goes.
If you intend to keep the lo-stall and short gears, a 650DP will perk it right up.

There are two times a carb needs to be evaluated; at very low-rpm like from idle to stall. and again over the top like from 5000 to shift rpm.
At low rpm, a too-big carb tends to be a lil sluggish, which is aggravated by small gears.
At high rpm. a too small carb runs outta breath before the finish-line.
On a streeter, you run outta road at 65mph, so running out of breath over the top never happens; so a too-small carb is better than a too-big carb.
But with proper gearing, say 3.91s to 4.30s and a 2800 or better stall, your engine never has to work at low-rpm, so a bigger carb can hit both bases.
With a 262 cam, I would recommend a Spreadbore type carb, to try and cover as much ground as possible. Plus a spreadbore with tiny primaries will offer the best potential for fuel economy..... if that matters to you. I like a metering-rod carb for fuel-economy runs because of it's tunability in that arena. So that sorta all points to a "goggle-valve" 650, if you are buying new;
or to a Thermoquad/Quadrajet/AVS, if reclaiming a used one. Don't overlook a Q-jet with Mopar arms on it; it is a pretty good design.
You can get a google valve with a phenolic bowl to help combat underhood heat, as to percolation and/or "vapor-loc"
The thing is, with a 262* cam, as to carburation, you can get away with murder,lol. Just about anything goes. The higher your cylinder pressure, the more you can get away with. Because the pressure increases the bottom end power and response, and gets rid of the mushiness of a too-big carb.

That long-winded post #20, will help you attain a ball-park tune, or prove you are already there. From there you get to play around some to adapt it to your particular combo. Hiway gears and a low-stall TC are always a challenge.
By the time you get to 3.91s and a 2800TC, the bottom end has long ago ceased to be a problem. You got a 360, so you are well on your way.
Once I got the tune right, my 276/286/110 cam is hardly noticeable.
My 270/276/110 cam was even less so.
Ima thinking your 262 will idle sweetly on 10/12 degrees Idle-Timing.
My 276* cam will idle just fine down to 550 at 5 timing, which is what it takes to satisfy the T-slot exposure. The point being; let the engine tell you what timing it wants, from the T-slot to mixture screw synchronization, and the freedom from tip-in issues..