One thing to watch out for with E-probes (active antennas) is that many design have no common mode isolation at the base of the antenna. And that apparently includes the L400B. In my experience, particularly in a suburban envirnonment, much of the noise I was picking up was conducted from the equipment ground in the house, through the coax shield, and right into the antenna. Adding an adequate common mode choke helped a lot.
And a few turns of coax over some ferrite won't do it. There are commercial common mode chokes that will do it; or a bifilar winding on a ferrite torroid or binocular core could do it; but you need several K-ohms of reactance to do any good. A signal isolation transformer will also work, but you need to feed the supply current around it with dc chokes (two; one supply, one ground).
I haven't tried it, but there are published designs using no amplifiers at all; just a step down isolation transformer at the antenna and another in the shack. I think it could work well.
Bob