You have been given some good thoughts re: things to consider. We just got into our hotel room, and I am finally at my laptop. Here are some more thoughts. Remove the fuel cap, as it is possible you have a non-vented cap which will allow the fuel pump to draw enough fuel to cause a vacuum in the tank and fuel supply line going to the fuel pump. The higher the rate of fuel consumption the worse the problem If that correct the problem replace your current cap with a vented unit. If the fuel cap is, by some chance, not the original cap it is very likely this is what happened, someone got a fancy replacement cap that is not vented, like for a 1971 or later Mustang, not knowing the difference in performance behavior with the two general kinds of caps.
Others have suggested looking for and/or replacing fuel lines, to include the rubber fuel lines at the carb fuel filter, the fuel pump (both suction and pressure side), and the fuel tank. Inside the tank is a sock filter that if plugging can be blown off if you leave the fuel cap off and blow some compressed into the output fuel tube (just a quick burst, otherwise you may end up with a fuel vapor fog all around you - not safe to do that by shooting more air than needed to blow the sock off the internal steel fuel pickup line.
Testing the fuel pump pressure and output volume is very important. Both tests are equally important. With the output volume test look for debris in the liquid fuel. Check and replace the fuel filter if needed. If your filter is the kind that threads into the carburetor inlet, remove it and see if you can blow through it. Any "significant" resistance indicates it is plugging or plugged. Be aware, if it is plugged there may be still more debris in the fuel tank, fuel lines, and fuel pump. If you use a tubing cutter to cut open the filter housing (not a hack saw, a tubing cutter) you can use a magnet to see if the debris is attracted to the magnet. If it is attracted to the magnet you have rust in the system, most likely from the fuel tank. Be prepared to have more filter plugging later if you don't replace or clean out the tank, blow out the fuel lines, and replace the fuel pump.
Another are to look at is the distributor mechanical and vacuum advance, especially the mechanical advance. As the RPM of the engine is increased, with the vacuum advance diaphragm disconnected thee timing should advance how fast and how far will depend on the RPM. I do not have any books with me with the specs, but I would be looking for at least 20 degree of advance by 2,500 RPM. If you are in that area you are likely fine. Otherwise the distributor may need to be serviced, re built, or replaced. The vacuum advance diaphragm ought not have any effect on timing at Wide Open Throttle, but it is still a good idea to test it for leaks or being ruptured.
Check the primary ignition dwell angle and/or point gap. If the point gap is too small the ignition coil will not properly saturate at higher RPMs. If you adjust the point gap/dwell angle, it will directly impact the initial ignition timing. So be sure to check and adjust the initial timing as needed. Check the spark plugs for proper gap. It it is an oem system you want 0.034" - 0.035" gap. Too little or too much gap will cause higher RPM performance issues
Finally, be aware a plugged/plugging exhaust system may be the culprit. If you have an exhaust pipe that is double wall piping the inner wall can collapse and cause restrictions. It is a long sho, but if everything else checks out that is an area to not overlook.
There are so many other areas to look at (spark plug condition, burning too rich or lean comes to mind). But, the preceding is where I would attack the problem.
Once you do figure out what is wrong please report back to this forum. I know I sure the heck would like to know what happens in the end.
Good luck!