Vacuum on 1968 GTS 340 4 spd.

Since you say you have proven the intake is not getting un-authorized air;
I'm gonna guess that your ignition timing ain't what you think it is and you have the additional problem of either;a lazy accelerator-pump system, and or a problem in the metering rod system, OR seriously wrong cam-timing.
Sometimes additional idle-speed can help, up to 750, but if that upsets the T-slot sync, then it just makes it worse.
I wanna go with cam-timing because Ignition timing alone won't usually cause this kind of issue. I say this because I have a dash-mounted, Dial-back, timing control with a range of 15 degrees, and when it comes to taking throttle,my engine cares not a bit about initial timing. The only thing that changes, with the T-slot sync properly set, is the idle speed and resultanant manifold vacuum.

nm9 outlined a nice test to check split overlap.This should always occur within about 5degrees of TDC on any one piston. I use #6, because of the ease of accessibility and the marks on the balancer are correct to be read there as well,after I have proved them to be exactly correct.The only street cams that might not be pidgeon-holed within 5 degrees are the thumper-style cams.If your Split-Overlap is outside the 5* then something is wrong.
I pull the intake, then lay a straightedge across the lifter bodies, leaning against the pushrods. Other guys turn the lifters upside down; that's just wrong. I move the crank back and forth until the straightedge contacts in 4 places, two on each lifter, then simply read the known-to-be-accurate balancer, looking for it to be in the target zone.
I know it's a lotta work, but after this, I don't have to wonder about it any more.
There is one wild card,
And I wouldn't have known about if it hadna happened to me.
If the you have a Mopar Electronic Ignition system; there are two types of pick-ups to signal the ECU. If you have yours wired in reverse polarity,you can make it idle, altho the reluctor will end up in an odd-sync. But it will not take much throttle and kindof stall there with some stuttering going on. As you relax the throttle everything returns to normal.
If you have your timing light hooked up, you can see what's going on. As the engine is being reved up the spark advance will go crazy firing at a multitude of wrong times, then when returned to idle, everything seems normal.
This problem is instant proof of a wrong polarity pick-up.
The pick-ups are color-coded , and the factory SMALL-block ones have one Orange wire and the other I have seen either black or gray. If at least one of them is Orange, then it is correct, and you can prove it by the spark pattern.

Good luck