I have built systems similar in concept to the one you are proposing. mine are for industrial automation.
We typically build machines with several three phase transformers and single phase transformers using the same connection to ground, and they are fine. even in buildings, there can be dozens of transformers all grounded to the steel (chassis ;) of the building itself. Each of these transformers interconnected to the same ground tie their respective neutrals to this point.
Barring being personally able to see what you are building, here is what i tend to think. just be careful, and don't proceed if you aren't sure what to do.
Any number of transformers can share the dashboard chassis, just so long as only one side of the transformer is connected as the neutral to it. that would be one side of a two-lead secondary or the middle lead of a dual voltage secondary. We use a lot of 12/24 volt secondaries. 24 v between the two black terminals, and 12 volts between each one and the centertap, with the two 12 v outputs opposite in polarity with each other.
what is important is to remember that in vehicles the chassis isn't a true ground, it's just an extension of hte return terminal of whatever power supply is in it. at 12 or 24 volts, it isn't a big deal, but at higher voltages you would HAVE to ground the chassis to avoid a potential life threatening shock hazard.
the chassis used this way is a shared return terminal to all the power supplies sharing it, and shouldn't interfere with each other.