The first question is: Do they sound boomy with other tubed/and or SS amps? And that word of caution is justified: unless you know a particular amp is stable with the ESL-57, don't take it for granted. The amp and or ESL's may go up in smoke.
Second, the HV power supply must be in good shape.
Third, if the bass panels are old and haven't been rebuilt, they will be boomy, because the bass film is not at the proper tension -- this ages/stretches or perhaps even gets tighter over the years. This is not a jab at VTA's tube kit or a Dynaco 70 or anything else here -- but on these older ESL panels, a SS amp will usually control the bass panels better and help with the boomy bass.
If on the original legs, which placed the speakers only a few inches off the floor, they could also sound boomy, especially if near a back wall. Side walls are probably OK, but keep them out of corners.
As far as the VTA board working with Quad ESL-57's: I don't know. I've asked this before on this forum and no-one chimes in except Bob, and he says he has some customers using Quad Electrostats, but doesn't say which. Magneplanars don't count either, as they are a (pretty much) 4 ohm resistive load -- easy load, but they like lots of current (I also have MMG's). Martin Logans don't count either, as their load is much more easy than an ESL-57. In fact, I know of nothing else quite like the Quad ESL-57 that is as difficult a load -- and Quad's ESL-63, 988, 989, 2905 or 2905 aren't as bad. So until I know of someone using the VTA board with the ESL-57, I'm not jumping on board....