I did try coating all three layers once and then expose with subsequent negatives for each colour, It was a complete disaster and I am not sure one would get acceptable results
For a multicolor print I also don't see how this would ever work. One of the main problems you run into is that you'll wash out one color from underneath another color - not to mention the fact that you can't actually get color separation this way to begin with as all layers will respond to all negatives!
The process may work for monochrome prints where the darkest layer (highest pigment load) is on top and the lightest at the bottom (lowest pigment load) and then expose through 3 different negatives with 3 different times. The 'underwash' problem should not exist in this case, although the (quasi)halftone screen nature of inkjet negatives may still spoil the broth and create problems.
AFAIK for all his multi-layer work people like Calvin coat consecutive layers and to the best of my knowledge this is also what he did for the prints he demonstrated in his Gum printing manual. Layers were brushed (not sprayed) with inert interlayers in-between to counter the problem of pigment bleed and thus get better hue purity/gamut. I know he did write a bit about the hypothetical airbrush spray approach, but ended up not doing that because of the obvious problem with dichromate toxicity (both acute and long-term) which will be a gigantic problem especially with exposure through the lungs. Someone has posted here on Photrio who tried this when he was young and it's kind of a miracle he lives to tell the story.
I can see why exposing everything in one go without wet processing steps in-between would be useful to maintain proper registration. The alternatives are pre-stretching the paper by soaking it a couple of times and hanging to dry in the same orientation before starting the printing process. I vaguely recall you
@Carnie Bob once writing that you do it this way; is that correct? I know that's one way Calvin describes it. An alternative approach would be to glue the paper to a dimensionally stable support like aluminum with something like unhardened gelatin. Then go through the entire printing process while keeping the wash water temperature below the melting point of the gelatin, and ultimately releasing the paper from the support by soaking in a warm water bath so the gelatin melts.
One thing to keep in mind as well is that Calvin has written a thing or two about how he develops his gum prints, a process that exploits pH as a variable to make the wash-out process very fast as well as very consistent.
The key question in the end is what problem you're trying to solve; then work out the feasible scenarios to attack it. I'm really not sure if a multi-layer, develop-at-once print is very feasible in a process like this. You end up having to develop (wash out) a fairly thick layer of material, which leaves the remaining image areas very vulnerable and susceptible to washing out. They generally withstand processing a lot better if they're allowed to dry out and properly harden after an initial wash.