I'd say...

a) Shake, or cut open that fuel filter... is it full of swarf?

b) Is the Carter a 'green' / 4070? If so, should be ideal... but yes, mounted down near the tank. I can certainly imagine that in certain high-load situations it might cavitate / have problems delivering enough fuel, if mounted high in the engine bay.

Or, as you say... might be the carb. The fact that fiddling with the filter seemed to fix things would suggest otherwise, though.

I also would clean the tank.

No idea if tank was ever touched up. Took several runs yesterday. No problem until 3rd run of the day, could barely keep her cruising on the level at 50 mph, finally slowed for a turn and then it took off and ran great, no reoccurrence, so it's very intermittent. I'd think if the filter was clogged it'd be more persistent. Oh well, I just created more pressing matters....tried to run a plug in the dipstick hole just to see if that's where a leak was...plug came out and I oiled the engine bay thoroughly! Might have to start a new thread on that one. This dipstick is weird.
Also I watched the speedo needle bounce and then fall to zero a minute ago......

The pump that is currently on there is of the solenoid variety.
Looks like this one.
Pump
Have the SU I took off, which is probably just fine too. Both were mounted in the front left corner of the engine bay, as high as the carb.

I would expect junk in the tank. Covers the pickup from time to time enough to shut it down or almost so then shakes off.

I'm inclined to think it's a tank/filter issue, too. I had the same problem. The car would run great around town, but as soon as I tried to push it to 55+ the filter would get completely clogged. I had a ton of sediment at the bottom of my tank. New tank + new filter = no more problems. If you have the old filter, blow some carb cleaner through it and see what comes out.

If it's the tank, then the filters will just continue to get clogged (at the worst times, I'll add). My second filter lasted all of ~40 minutes of drive-time before it got stopped up.

B

I had this problem years ago when I drove the car. I bought one of those clear glass filters that you can take apart and clean out. I put it right before the pump. You can just look under there and see how bad it is.

The filter I took off was see through, looked fine paper is a bit discolored. One I had on hand was a canister type so it is on there now, can't see into that one. I'll back burner it for a while while I tinker with other things.

Finally got around to moving the pump and it had no effect, that is still very low volume of fuel delivery-7gph. I figured I'd start with the pump move since it "should" be back there anyway. I had to cut the fuel line from the tank right near it's outlet (leak in the metal line) and I caught some gas it looked TERRIBLY dirty to me, I let it evaporate all day and the pan has a nice brown powdery crud in it. So it looks like I'll be dropping the tank next. Although I'd think it would eventually totally plug up or drop so low as to make it undrivable. This is not the case. I can run down the highway at 70mph for several minutes, then a bit later struggle to keep her going 40mph, could this be filter clogging and unclogging?
No matter, tank must come out and get treated, all filters replaced, then start over.

Yep, I would also bet that it is the in tank filter cloging and uncloging. Pull that tank have it cleaned and lined.

If your tank is rusty inside, you need to address it before driving too much. Loose crud in your carb will make it a bear to dial in later down the road. Seems you can never totally clean the small passages out. Rusty tanks have caused a lot of fuel delivery issues in many types of older cars.
JC

This could explain why the primary barrel on the Weber always looked so carbony, although the inside of the carb looked pretty good, likely thanks to inline filters. Alright, I'll drop the tank and fire up the grill. I have a Kreem kit already so I'll use that. That and new filters "should" resolve the fuel supply issues. I'll probably just nix the in tank filter and have an inline one right outside the tank, another just before the carb. As long as the original 1/4" ID metal lines are good yet, I assume I'll get close to 15 gph at an acceptable pressure after all is done.
Maybe if I'm lucky I'll be able to start tuning this thing before winter!

Make sure you are feeding the weber through the supply line and not the fuel return line. (assuming you have a DGV) Pull the lines off. One side will have a restriction in the line and the other will be wide open. The restriction is for cars that have a fuel return. Mine doesn't, I don't know about yours. Anyway, I made this mistake and was trying to push fuel through the orifice and had plugged the wide open inlet. The orifice is about 0.060" or so.

Just a thought,
JC

Interesting on the different inlets. I assumed they were the same, just right or left for different applications. I was going to move the inlet to the other side to get the supply line away from engine heat but now maybe I won't. Both Weber's I've dealt with had one side still "plugged" (as in never opened after the casting). Ironically my last Weber (38/38) had the inlet on the wrong side (its right), I moved it to the other with no negative effect. This 32/36 is on the carb's "right side" but should really be on the left/outboard side. Not a big concern though.
I suppose if you buy the Weber DGV for a certain application, it would come with one side or the other opened.
Anyway, my fuel flow measurements thus far have been right before the carb and it's a trickle, measured at 7gph. Where exactly the hold up is I don't know but since new inline filters didn't do it, and different fuel pump didn't, and moving the pump didn't I'm assuming the tank filter itself is clogged. There were actual chunks of goo that shot out when I cut that line.
Be nice to put this issue to bed and move on to the next. Soon I'll have this thing totally road worthy (although I've put 1200 miles on this summer as it is!)

Your engine consumes the same amount of fuel at a given RPM wheither the car is in 1st gear or 4th gear, so I'm wondering why the difference. Are you sure the ignition timing is correct? At cruise in 3rd or 4th you'd be seeing a lot of vacuum advance and then drop it back as you opened the throttle. I think I'd have the distributor and vacuum advance unit checked.

Oh sorry about the bum advice. I guess I should have read the whole thread. Good chance it is the inlet in the tank. You may have trouble with that after you seal the inside of it too. That is why I just bit the bullet and bought a new tank and sender from VB right after I bought the car. The PO had put a bunch of filters in series before and after the pump trying to capture the rust...lol What a mess.
JC