I had a similar problem with my 1960 bugeye. I've been meaning to post something about it, but it's a long story, and I didn't have much time. Your similar problem has pushed me over the edge.
My car had a transparent fuel filter just ahead of the carbs. It was full of fuel when cool, but when the car warmed up, it formed a huge bubble, filling most of the filter--I was amazed that fuel was getting through it at all. When I stopped at traffic lights, though, the thing would start to sputter and almost die--speeding up the engine kept it running, and finally it smoothed out--at least until the next light.
Close inspection showed bubbles coming up into the filter from the fuel pump. A fair number of them. No sign of any leaks that might cause air to be sucked into the line--one solid copper fuel line from tank to pump. All of the last few connections were quite tight. So, I suspected it was fuel vapor, not air.
At that time I replaced the mechanical pump with an electric one, mounted near the tank. It had a fuel filter at its input, so I figured the one near the carbs really wasn't necessary. When I removed it, I temporaily installed clear vinyl tubing instead of the usual black rubber fuel line, just so I could see what was going on.
Wow, what a surprise! When the engine was hot, the fuel in the lines looked like champagne--lots of very tiny bubbles forming, coalescing into large bubbles which settled at the high point of the arched fuel lines. The big bubbles did not blow through the lines, and mostly filled them--again, hard to see how fuel was getting through at all. Now, no bubbles were coming up from the fuel tank, though--it was all forming high in the lines.
I noticed that arranging the lines so there was no arch--i.e., the fuel flowed continuously upward, allowed the bubbles to rise to the carbs and blow through the vent in the carb bowl. Once the lines were arranged this way, I tried reinstalling the fuel filter that I had removed, but it formed a vapor bubble again, as before.
So, now, I've reinstalled the rubber lines. The fuel line from the tank goes to a tee, then straight vertically to the carbs. No fuel filter at that point. I keep the lines away from the engine, to keep them as cool as possible, and so far no more problems.
I suspect that today's fuel vaporizes more easily than the leaded stuff common in the 60s. Perhaps more volatile substances are used to increase octane--I've heard that butane is one substance, which is obviously more volatile than tetraethyl lead. Then, the fuel line goes right to the pump, mounted on the engine, which is hot enough to start the fuel boiling. Also, I suspect that the vapor just doesn't move well through a wet paper filter element, so you get a bubble forming in the filter. Some fuel is absorbed by the paper, and blows through with whatever vapor gets forced through by fuel pressure. But, it's not enough sometimes, and the whole situation is really an invitation for trouble.
I plan to put some insulation around the fuel lines, at least in the engine compartment, sometime before next summer. Ugly, yes, but reliability is more important to me right now.
So, what to do in your case? It's a real dilemma--you really need a fuel filter somewhere, I know, but the bubble problem (which, I suspect, is probably vapor, not air) is a serious one. Maybe locate it near the tank, where it is cooler, or use a screen instead of a paper-element filter. I don't know your car well enough, so I can't suggest much else.
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