The Eddy 500 is a good carb but out of the box they are setup pretty crap, the floats are always miles out for starters. The jetting ain't that great for a 3.5 lump either.
In my humble I reckon that your regulator is not only controlling the pressure but also the volume of fuel which is no good. I run a low pressure pump which means that I don't need a regulator. If your pump is less than 7 PSI ditch the regulator. A bloke on the Cobra forum had all sorts of issues and it was the regulator.
A simple test is to disconnect the fuel feed to the carb, and bung it into a 2 litre container (Cleaned out milk containers are good for this). Run the pump for exactly one minute then mark the fuel level on the container. If you have a good way of measuring the volume then measure it. If you won't then do the following.
Drain the fuel out of the container and re-fill it with water up to the mark. weigh the water on some good kitchen scales, every gram of weight will be 1cc of water and hence fuel. (Roughly!)
The formula below will tell you whether the fuel system is up to the job:-
BHP= (Vol of fuel per min)/4.7
Or (Vol of fuel per min) = BHP x 4.7
A hot 3.5 might make around 230 BHP, it would need 1081cc's of fuel per minute to make this BHP. Really in this case you would want the system to deliver at least 1300cc to give some safety margin.
You can try the same test without the regulator fitted.
The bloke on with the Cobra quickly sussed out his problem using the gumph above.
If you think that the fuel pump is somehow slowing down when it gets hot you could run the pump for 5-10 minutes into a large container then run it for 1 minute into the milk container.
By the way a good starting point for the jetting would be 86 primaries, 67-55 rods, silver springs, and maybe 83 secondaries. (I'm a bit reluctant to recommend secondaries because if they are miles out then you could blow the motor)
My mates fairly standard 3.5 needs 83 seconardaries as does Muscle Manta's stage III 4.6. My stage III 4.6 needs 66 secondaries. (Which I had to make!

) Both the 4.6 lumps run 86 primaries and at the moment 69-52 rods, we are going to try 69-55 rods. You can not buy these rods, they are home made. 69 is right on the limit for the cruise on our engines, they are fine with 69's but 'un-drivable' with a 70!...only 1 thou difference!