I have a 1985 Land Cruiser FJ60. Long Story short we’ve rebuilt the engine, Transmission and lots of other major things in the car. I had the carburetor rebuilt about 6 months ago to try to get more power out of the engine. Since doing this it’s had this crazy hesitation that happens when driving the car at high speeds for more than just a few minutes. We’ve since put in 2 more new carburetors and have gone through every system imaginable to try to figure out what’s causing it. 6 months and about $4000 later we still can’t figure it out. To me it feels like it’s a fuel issue but that whole system has been gone through by 2 different mechanics. (The first mechanic gave up) 
It basically feels like you’re running out of gas and it’s sputtering. Could there be some sort of vacuum created in the fuel lines when the accelerator is held down for a few minutes? maybe that’s why it can’t be detected when the car is not under strain? any other ideas?
Has anyone checked that the vacuum advance in the distributor is operating properly?
Tester
yes but keep trying
High speed driving stresses some of these functions below, so, beyond what’s already mentioned, worth checking
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Since it happened with the carb rebuild, first I’d focus on Carb Power valve/metering rods. No experience w/your exact carb, but it almost certainly has some kind of method to increase fuel flow beyond how it is configured in normal operation for high fuel flow situations, like high speed. On my Ford truck that’s done with a “power valve” which bypasses the normal jet; but some carbs use metering rods which partially block the jet in normal operation, and are supposed to lift out of the way when more fuel is required. The force to do that usually comes from a vacuum signal I think. Since you’ve replaced the carb several times, more likely the problem would be that the vacuum signal isn’t working for some reason. In an '85 there could be an electric solenoid involved too.
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Problem with carb float mechanism causing the fuel level in the bowl to be too low. Carb performance is very sensitive to this setting, esp at high fuel flow. You might just want to experiment moving the fuel level a little higher, see if that helps. Could provide a clue to what is wrong.
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Venturi feed air bleed is too big.
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Main jet is too small.
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Do you have a fuel system specialist shop in your area? There’s so many things that can go wrong if a carb isn’t rebuilt correctly, or you’ve got the wrong carb configuration for your engine, sometimes it is best to bring in an expert. There’s a place called “The Carb Shop” , I think it is in the Los Angeles CA area, that I think you can mail your carb to, and they have carb experts there who can pretty much figure anything out involving carbs. For a price of course.
If it isn’t the carb, and the carb rebuild involvement turns out to just be a coincidence …
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Something is clogging the air intake system. Blow out all debris from right where the air first comes in, probably near the front grill. & make sure the engine air filter is clean.
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Something is clogging the exhaust system. May have to start taking it apart to find where the clog is. The test for an obvious clog in the exhaust system involves an intake manifold vacuum reading. Sometimes when rebuilding an engine a gasket will shift during install, and partially block the exhaust or intake manifold port.
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Too much intake or exhaust valve clearance. Valves aren’t opening all the way. Check valve clearances. Check valve timing while you are at it.
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Distributor/coil problem. Ask a shop to do an o’scope analysis of the ignition system at high rpm.
Edit: You probably already know this, but since you own a Classic Land Cruiser, there’s at least one magazine I’ve seen that is geared to that exact topic. Surfing through the index for articles on your problem, or just seeing if one the advertisers there might be able to help you.
You’re wrong George.
The acceleration on your truck is done thru the accelerator pump on the carb.
Once the accelerator pump adds the extra fuel under acceleration, the power valve continues to add fuel until you release the accelerator.
Tester
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Do you hear air hissing when you open the gas cap? Poor venting can cause high speed hesitation. If this happens every time you drive at high speed, wait until your gas tank isn’t full an remove the gas cap. If this doesn’t help the hesitation, at least you have eliminated it as a suspect.
The curious thing about the OP’s problem is that it remains after multiple carb replacements. One thing that could cause that is there’s dirt somehow getting into the carb from the fuel line or sucked into the intake air path. So you install the new carb, crank the engine, and it immediately clogs the carb passages. Some of the air and fuel passages in a carb are very tiny, and even very small particles will clog them up in no time. Taking all that stuff apart and cleaning it out, making sure the fuel filter and air filter, and the fuel an air entering the carb, are all pristine might help.
Tester … no disagreement on your comments about the operation of the Ford 2100 carb, both the accel pump and the power valve are involved in rapid accelerations, with the accel pump responsible for giving the initial burst of fuel, and the power valve to sustain it. There’s no metering rods in the 2100, those came later, w/the 2150 I think. At the time my truck was manufactured there was a fuel crisis, and gas became pricey, if you could get any at all; so Ford didn’t call it a power valve, they called it an economy valve, or something like that. It could be called either, since it opens (for power) during rapid accelerations , but closes (for economy) otherwise. What to call it depends on what you want to emphasize, power, or economy.
This all reminds me that some carbs of yesteryear used a different technique called a variable venturi to increase fuel flow during times when it is needed. If OP’s truck uses that type of carb, a problem with that function could cause this too.