Let's start with the premise that a campaign is about a group of players. It doesn't have anything to do with the setting, rules, or characters. I've been in campaigns where the character mix was almost completely overhauled, where one rules set was dropped in favor of another, and where the PCs relocated from a homebrew setting to published setting. So a campaign is the label for a group of people agreeing "unless we later negotiate otherwise, this is what we are playing for the next X sessions". Nothing more.
Given that definition of a campaign, here's my idea: three settings, three sets of PCs, three similar but not identical rulesets, one campaign. We start with 1st level Eberron PCs and play through a module. When that module is done we whip up some starting Arcana Unearthed PCs and play through a single AE adventure. Once that is done we play one Iron Heroes adventure with a third set of PCs. Rather, rinse, repeat until we've exhausted all available modules. If along the way someone realizes that they don't like one of the three settings/rules we're using, we can discuss that as a group. Everyone at my table is a grown-up. If someone isn't having a good time I want to hear it and try to resolve it.
Eberron has four short published modules and Dungeon adventures, as well as being fairly conducive to adapting other D&D stuff I have laying around. I've got three AE adventures, two of which are substantial. A few others are floating around out there. The weak link is Iron Heroes, with 2 medium-sized adventures. We may run out of IH stuff before we're done with the others. Since I'm proposing playing IH third, I'd be happy as a clam to reach the point in the campaign where I need more Heroes adventures; that would mean the campaign was chugging along at a goodly pace. Around that same time the Eberron PCs will hopefully be approaching the right level for Red Hand of Doom. If so, I would like to conscript Doug to run that adventure for the Eberron section of the campaign. That would give me a break and hopefully sufficient time to write and/or adapt some material for Iron Heroes. And I would get to play a robot for a while.
My one concern about this scheme is that Doug is the only player I know that has copies of all three of the key books. As I understand it a PC built from the D&D corebooks (and associated splatbooks and whatnot) is still pretty functional in Eberron, but the other two settings absolutely require access to the book to build the PCs. I absolutely loathe the concept of the "chargen session" because in my experience it is a good way to start a campaign on a downer. In games with wildly random chargen they can be fun, but for any sort of points-monkeying game the chargen session bores me to tears. I also abhor the idea of asking players to buy big expensive hardbacks just to play in my crazy campaign. Hell, I didn't pay for IH or Eberron, why should they? But they seem to be more eager to buy big shiny hardbacks than I, so maybe I'm seeing a problem where none exists. I guess Doug and I could knock out some 1st level PCs for the whole party after a little Q&A to establish the general parameters of what everyone wants to play.
Now, you've probably come to the conclusion that this is a pretty complicated way to avoid having to pick one of three campaigns. You'd be right on that point. But for me this crazy plan offers some advantages over a more traditional campaign structure. First, we get to try triple the settings/rulesets in the same time. Second, jumping from setting to setting will help me keep my short attention span engaged. And third, we could prolong the period spent at low to mid levels, the part of the game that interests me the most.