Alarm Clocks for Heavy Sleepers?

jonadab asks: "I'm a heavy sleeper. I wake up gradually. Sometimes it takes quite a bit to get me cognizant in the morning. I've been known to sleep through alarms entirely, or shut them off before fully awake and later not remember doing so. It's not that I don't get enough sleep (I go to bed at night when I get sleepy), but my body tends to want a day longer than 24 hours, and I have to use an alarm to keep myself on a constant schedule with the rest of the world; otherwise, I get up a little later each day and pretty soon I'm sleeping till noon. So I'm always in search of a better alarm clock. Maybe some of you have experience with alarm clocks that you particularly like"

"Here are some features I'd particularly like to have (though anything that's good at waking a heavy sleeper is worth mentioning, even if it doesn't have all these features):

• Gets progressively louder until snoozed. Starts louder with each successive snooze.
• Max volume slightly painful, but not physiologically dangerous. An air compressor and train whistle is probably overkill.
• Easy to snooze, but hard to accidentally turn off completely. Bonus points if turning it off means being cognizant enough to operate a screwdriver or tool of some kind.
• Snooze time gets geometrically shorter each iteration (e.g., half as long as the previous) so that there's a maximum total snooze time that can be approached assymptotically.
• Has battery backup so that it will operate during a power outage, at least to keep time. (I _could_ just stick it on the UPS, but do I really want to spend a UPS outlet for an alarm clock?) This is a feature my current clock has (takes a nine-volt battery), but even better would be a rechargeable that will even operate the alarm during a power outage.
• Can be set to always go off at the same time every day, so I don't have to remember to set it at night unless I need to get up at a different time than usual.
• Has some kind of cool feature with geek appeal -- but not binary time display; I need to be able to read the time when mostly asleep.

Cost does matter, but I'm willing to pay somewhat more than the going rate for an ordinary alarm clock, because this is obviously a bit of a specialty item. But I don't want to pay a totally outrageous sum; at worst I could build one out of commodity computer parts and a nice set of speakers for probably three hundred bucks or so, so please, nothing more expensive than that. Bonus points if it's more like $50-75."

If you were going to go the route of building a cheap computer to do this, what software would you use to do it?