[Lynn Eades]

If I recall, the 94 and 97 stromberg carbs are delivered fuel at 2 1/2 to 3 1/2 psi. any more and the carb will flood. This pressure is achieved solely by the spring under the diaphragm in the mechanical pump.
If the carb is flooding from the electric pump when the engine is stopped, why wouldnt it be flooding, when its running (and vibribation is also happening)
There are three things here. delivery pressure, suction (the ability of the pump to lift the fuel to the pump measured in inches of mercury or the metric equivalent) and lastly the delivery volume.
It sounds to me, that you have too much pressure and not enough volume.
If you put a test gauge on your delivery pipe to the carb you can check the delivery pressure directly. If it is too high that will cause your carb to flood, and that can be a little tricky for even the mechanics among us to diagnose. (we can often wrongly decide its starving) Many of the electric pumps will deliver a hansome pressure. I saw one advertised recently at 8 1/2 psi. (Alfa Romeo used to have an adjustable pressure regulator called a "Fisba" for the carbs (Delorto, Webber, Solex)
My gut feeling is that you might have an air leak into the lines somewhere, between the pick up(s), and the pump suction side. these can be difficult to find. One of the prime possibilities will be the fuel change over valve (assuming you have one)
The best way to check this is run a temporary line (reservoir included) to the pump, and see how she goes.
If that fixes it, re introduce what ever sections you can, until you find the leak.
You could use a vacuum gauge on the suction side of the pump. Get a reading, and see if its the same at your fuel pick up pipes at the tank(s)
On the vapour lock, The original lines were steel not copper. This might help to slow the rate of heat transfer. Making up the pipes with the risk of vapour lock accuring in mind, might help.I have seen some really bad results.
Lastly, I would check that you have no blockages any where in the lines. I know a lot of it is new, but it is amazing where swarf, solder, thread tape, silicon, and every other type of gunge can get to, in a new system.
Hope this helps when your lost for ideas.