As someone who has made some fair attempts at plumbing, tank repair, and silicone application without much fail, I'd say it is plausible if you can assure that there won't be movement and breakage.
The bridge is a great idea. I actually have seen one with cichlids between two 55 gallon aquariums in a restaurant that took the fish across the ceiling and was big enough for 9 and 10" cichlids. The thing is amazing. I tried searching with 7 different search and couldn't find it after 30 pages each time. I wish I could find it again. I recommend the bridge if you plan to get it below water level enough to avoid air exchange. I've heard the spill is insane if the air comes in too fast. That may depend on the amount of water in the tunnel and how much room there is for this amount of water in one tank. I say one because it may not disperse equally to both tanks.
As for problems with acrylic and developing a secure mount, use plumbing supplies to create pressure on both sides of the tank walls. Put a threaded adapter on the inside of each tank and then connect with the female threads of 2 more adapters to the outside. PVC can be cut with a dremmel, handsaw, circular saw (USE A VICE OR LOOSE A FINGER), or even a jigsaw. I use a dremmel because the blade is easier to clean and it won't get stuck as easy because of the wider clearance. Once you have a path way to the outside of each tank, you should be able to use silicone inside the slip joints of the outside adapters. Although silicone may not stick, enough of it will pressure seal and the joints for 3+" tubing typically have at least 3-4" of slip. In addition to silicone, PVC cement is a candidate though I haven't tried it with acrylic. If it is enough of a plastic, it should be fine. Don't worry about toxicity because once the glue is dry, there are not hardly any toxins. For example, water remains drinkable an hour after the plumber leaves. I had called the company once upon a time asking for specific information regarding the amount of time to wait, percent toxins, cleaning, and dangers concerning the glue in regards to myself and fish. Basically, the glue and primer just have to be dry. If you want to be careful like me, just run water through it for a day. When I installed my sump, I cycled the water, replaced the water, cycled again, and then tried feeder fish. No problems. I was able to feed the fish to my leaf fish and still no problems. Now that I'm off topic, the aquariums have secure pathways to the outside with pvc threaded adapters (Put silicone on the inside glass pane under the adapter when you go to tighten). The tube will mount in between using either silicone or PVC cement and you will have been cycling water and checking for leaks. Assuming the water pressure is not to high to burst the acrylic pipe(s), your dual tank should be in good shape and ready for fish after your nitrogen cycle.
Btw, was the glass shop able to cut the glass? I know glass shops typically shy away from finished products that they don't install or build themselves. If they say no, use a circular drill bit that is for all purpose applications and go very slowly. You have to let the start go in first, and then you have to let the rim cut evenly. A drill press would help if you have one and the tank will fit. the pressure may be rough on the aquarium from the bottom where it lies on the stand though. There are some youtube videos of this if you want to see how it gets done.
http://www.youtube.com/watch?v=OvMkwVPSC50
Just as you said, you will need a solid base for the dual tank to sit on literally as you connect them and for all time after that. Too much of a jar or bend on the seals will cause leaking and maybe break either tank or the tube(s). 3/4" plywood would be a good choice and if you can find a welder, metal would be better. You could use the same frame as the tank bottoms. The 90 degree bars would simply be around the perimeter of both tanks with the long ends between the outer corners of both tanks.
Just a thought, filtration will always be weird with these kinds of tanks. If you have the money, get a can filter and put the inlet(s) in one tank with the outlet(s) in the other. Filtration will be better though circulation will be in only one direction. Regardless, I think that is typical of an aquarium. From what I've seen in forums before, adding food to both sides will keep the fish in both sides. If you use something other than a can filter, filtration may not be as effective because the water in the middle will most likely be pulled equally to both sides and therefore not be filtered or oxygenated. Someone may be able to contribute to this with more experience on the issue but this is what I had in mind as I was walking through the build above.
Feel free to try this at your own risk, I haven't done this exact thing before but I have worked with plumbing through the glass of a tank as well as PVC cement on an aquarium application. 10 gallons shouldn't be rough though. Make sure you use clamps or measuring device that isn't as movable so that you can get your holes to line up and the aquariums to rest evenly and equally on whatever support you choose.
