Is it possible to increase maximum seatpost insertion length by filing down a seat tube bottle cage mount boss?
Drilling the seat tube is a bad idea, for the reasons you've indicated. Very rarely a bike shop will have a tool for reaming a seat tube (more usually framebuilders have those) that can to the task in a slightly safer way.

BUT from my experience with a welded steel frame where I didn't bother to back-purge (lesson learned!), even once you weld an extension onto the end of a half-round file, it's a tedious and difficult job to file down irregularities inside the seat tube. You're trying to apply pressure half a metre away from the part you're holding, and that's hard to do. You need a long, strong extension on that file. This is why framebuilders have seat tube reaming tools (which are expensive).

A reaming tool will probably not help you, because that boss is a single, hard obstacle and will likely damage the tool if you can even get it into position to cut the boss. If you do get it in there it's as likely to cut the opposite side of the seat tube away as cut the boss.

A better approach would be to drill out the boss. It's likely that the boss is actually a separate assemble riveted into the frame - they drill a hole, insert the boss, then compress it so it clamps into place. If you can drill out enough of the boss it will fall out, leaving you the original hole in your frame.

Which is the real problem with this approach - at best you'll end up with a hole in your seat tube, and the BB will fill up with water. You can out tape over the hole, and replace the tape when it starts to fail, but it's not ideal. Welding a cover plate on will reverse the heat treatment of the aluminium, leaving a soft spot in the tube. Soldering a patch on would be better, but soldering aluminium is hard (it's an excellent heat conductor!)

The extra stress from the end of the post should be minimal, most seat tubes are actually butted so that minor bends or dents to the tube don't lock the seatpost in place. You'll find the top 100mm or so is tight on the post, after that you have 0.1mm or so space around the post.