Hey Dan,
I was thinking along the lines of a turbo for cars but those all have 90 degree off set flow, with some really intricate machining you could get it to be axial flow but it would be a pita, so then I was thinking of how super chargers work with a worm gear type pump, again some heavy machining to make it work but thats a great example of an axial flow compression. Then of course once the words axial flow entered my head I thought how stupid I had been, lol I am a gas turbine mechanic for the navy, all of our gas turbines (jet engines) are axial flow, well for ship main propulsion anyway. Your idea for a set of stationary blades and two revolving blades has the right idea just needs a little tweaking. On our turbines between the blade tip and the casing we spray in a foamed aluminum, when the blades rotate the first time they cut into the foam and create a seal so air cannot travel backwards, each set of blades is slightly smaller than the previous set which causes the compression of course, but since the outer edges are sealed the air has no choice but to move forward. Our compression ration by the time it makes it all the way through the compressor is 16:1. Here are some pics from the GE LM2500 which is the workhorse of Destroyers, Cruisers and Frigates...
The green section is the stationary blades, they are attached to the outer part of the turbine assembly, the gold blades are the rotating ones and they are all connected to a central shaft. Obviously this is a cutaway.
A real one that has been opened up along its center line
An Exploded diagram