I hang everything using 18 gauge staples (5/8" in solids, 1 1/4" in MDF) in the "unseen" end of the cabinet door; top of uppers/ bottom of lowers. You have to have a stapler without a "bump safety" and shoot from a distance to leave a portion of the staple exposed, practice on scraps

). Attach a rotating hook (with positive stops at 0, 90, 180 and 270 degrees) to the ceiling of your booth, hang the doors from "hanging wires" (made from heavy gauge coat hangers) and shoot away...
You'll need to make a dedicated "drying area" with a custom built rack to allow for hanging numerous doors/end panels/fillers etc until dry. I make these from 3/4" plywood (lag bolted to the ceiling) with "teacup hooks" spaced @ 4" o/c. Large panels, (i.e. fridge gables) get a 16-20" long cleat screwed into the "unseen" end and are stood on empty "fiver's" in the booth...full height fillers/top rail get the same treatment but you can staple the cleats on, as opposed to screwing them. This method allows for full "wet coats" on larger objects without the attendant overspray problems (as long as you shoot from bottom to top, starting with the largest side to be finished, carry over the top (front edge of the gable) and finish the other side top to bottom)...
What products are you using? I've used these methods with
very demanding high-solids post-catalyzed conversion varnishes (i.e M.L. Campbell "Resistant") and achieved very good results...
Please note...there is a significant "learning curve" when shooting large,
smooth surfaces vertically with
any high solids product.
Stain grade doors (done with a wiping stain) get stapled prior to staining; both sides and all edges can be done at once...Important: check for drips/runs from the joint between the center panel and rails/stiles after hanging them vertically;
check all round for wiping marks...glaze wipes are the same, you can do the whole door at once...spray staining...ditto...
The "cleat method for large panels" (described above) can be problematic for spray staining, this due to "bounce back"/"haloing" issues. These are usually spray stained flat (for the fully exposed side)
then cleated and finished...
...I ran a "very high end" (albeit small) custom finishing shop for years and these methods are tried and true...my 360 degree hooks were on an automated "track line" so all you had to do was stand in front of the booth face and spray; this minimized all the "handling" time. A track line is a significant investment however...the entire room (25x40) was the "booth" with a large make-up air unit/heater on the back wall and a 7'(h) x 10'(w) "filter wall" at the front.
All that said, I
still hang everything I can when dealing with cabinet doors; the finished product and ability to "wet coat" all sides is well worth the minimal effort it takes...
...SLS; it looks like that product you linked to will only work with "euro" hinges? What about the "shadowing" behind the hanger? How many doors can you shoot before that hanger has so much paint on it that it's useless? Coat hangers are $1/dozen at the dollar store...
Cheers, Ron