From what I can tell on the image I have seen of the JVM410H, there are no tube shield holders on the 12AX7 preamp tubes. In reality, they are not really needed especially if the tubes are facing upward. However, I would suspect the Mesa 6L6GC tubes to be more of the contributor to noise than the tube shields. The only amp that I have been able to use the Mesa branded 6L6 tube in is the Roadster but I have had new tubes out of the box vibrate terribly (internal structure causing tube sing) that is noticeable at low volume on a clean channel setting. I also have the same issue with the last set of SED =C= tubes (both EL34 and 6L6) that were prone to this issue as well. If the power tubes are of low quality or poor workmanship in their construction, chances are they will resonate at certain frequencies due to change in electric field similar to piezo effect that is common with large sized ceramic capacitors. There are some 12AX7 tubes that will make mechanical noise that will actually make it into the electrical signal. Most prone are the long plate 12AX7. However, the JJ preamp tube ECC83 also used by Mesa can make noise due to the getter construction. I have a few of those that are very noisy. I generally weed those out of use (finger tap test usually works to find those noisy ones).
The issue with the tube shields, they are simply an aluminum tube with a partially closed end but still open. Sure the spring will make noise when not compressed but the tube shield in itself can resonate at certain frequencies (probably only relevant in a open back combo amp vs a head) based on sound pressure change. The longer tube used for V1 that may hide behind the OT would be more prone to vibrate at lower frequencies vs the shorter tube shield. One also has to consider the surrounding environment too. I have my Mark V combo and the RA100 combo in my family room, not the best place for playing due to the large assortment of decorative glass bottles my wife had collected and arranged on a build in cabinet that extends from the floor almost to the celling, also note that this particular room has a cathedral ceiling which crests about 25 feet above the floor, and what makes it worse, the brick fire place and structure encompasses nearly one wall of the room. Often when I play through either amp, I hear rattles and odd noises that sounds like it is coming from the amp itself, even think the speaker is buzzing. In reality, the noise is coming from the bottles, shelves and even the pictures hanging on the walls. When the amp is removed from the room and placed in the studio, I hear different noises but not from the amp, it is coming from the ductwork and register on the floor near the window. Take the amp outside and see if the noise is still there (assuming you can do this) or in a dead room (was thinking of modifying the bedroom I am using as a studio with foam wall panels just for that purpose).
It is what it is, worse thing to do is to play your amp in a room with an acoustic guitar sitting out on a guitar stand. If you want to hear some earie sounds or strange slapping noises, it will be coming from the acoustic guitar as the strings will begin to vibrate. Been there done that (at first it freaked me out as I had no clue what the noise was and where it came from but did not take long to realize it came from the 6 or 12 string I had out at that particular moment). Acoustic drum sets, especially the snare drum will make some nasty noises too caused by sound pressure variances, found this out when I was practicing alone without the drummer or bass player. WTF is that? first thought the amp was crapping out.