You can actually use way more than a meta http-equiv to communicate the purpose to search engines, and while you may want to geo target in WMT, you may also want to have a 'worldwide language based target' rather than limiting your target for a language to a country... Links and Search Engines
I actually don't see any issue with the first approach other than being confusing to manage and to visitors... If you can use all three extensions on your server, then it's not going to cause your server any issues for you to use them. It's no different than using js, php and html (or asp, php, htm, js or php, cfm, js, css, htm, inc, ico, gif, jpg, jpeg, fla, swf, txt, png) extensions on the same server, and with the number of sites and software installations using page.php.something.else or page.cfm.stuff-here?otherstuff I can't see how 3 different extensions would cause any more issue for a server.
As far as duplicate content with the index.ext goes, you run into the same duplicate content issue with a single extension if both the root domain and the index.ext are accessible, so you have to redirect one to the other anyway, and it's easily overcome, but you don't have 'triplicate content' because each index.ext is treated as a different location. index.htm is not the same page as index.html and if they have different content (even language interpretations) they are different pages and not duplicates.
There are also site redirecting to http://www.example.com/index.ext rather than serving the content at http://www.example.com/ and I've seen one in a very competitive niche doing very well redirecting the root domain to /page-name, so you DO NOT need to redirect from /page-name to the root domain for ranking (or any other) purposes, you just cannot have the same content available at both locations. (It bothers me when people redirect the root domain to a page name, but it's not an issue with search engines at all.)
Robert Charleton even said you could designate the language in the page name, and a different extension is a different URL, meaning it's essentially the same, because each different extension is treated as an independent location, whether the location changes from the information before the . or after the . is really irrelevant. Any difference in location is a different location. You could actually have three different languages on your site by different capitalization: Page.html page.html pagE.html Those are 3 different URLs and would be treated as 3 unique locations by search engines and they would be very confusing to visitors and to manage, but you could still communicate the same point with the exception of not being able to designate a geotarget in WMT.
If you can designate a language difference between two pages ending in html because they're in a different directory, then you can certainly designate a language difference for two pages that don't have the same extension and have search engines figure it out...
If you want a conservative approach, or geo targeting in WMT (personally I wouldn't use it), use one of the other ones suggested, but if you want something different and don't need geo targeting in WMT there are plenty of ways to communicate your point and 'silo' your link structure and navigation so search engines understand what you're doing.
I'm sure there will probably be more people saying you can't use extensions to do what you want, and we'll have to just agree to disagree there, because I think you probably can and actually like the idea myself. But I do go by TheMadScientist here, so I'm probably a bit nutty or something and it might be better for you to 'follow the crowd' than to do anything different or new you thought of by yourself...