I don't know how to sort your particular problem, though as I understand it that folder is where apt stores local copies of stuff... which isn't by itself very helpful...

I presume you've done the basic stuff, like running df to see what sizes various partitions are limited to inside the chroot itself (maybe /var is limited to a fixed size?), ls'ing and du'ing inside the /var/cache/apt/archives folder to see how much data that folder has by itself, and if there's anything which looks like it might be worth deleting, etc? (On my actual standard Debian Wheezy laptop install, that folder has 1.6GiB of .deb files, hardly necessary to keep lying around.)

So presuming you've done all that, my next guess would be to figure out where and how the 'self growing' chroot filesystem is hosted on the N900's filesystem. I've never done the whole Easy Debian thing, so I may be completely wrong here, but if the chroot filesystem is stored in one big file which itself resides in top of the MyDocs partition, and if that partition is still formatted the way it is by default (with that lame Microsoft filesystem which can only hold files 4GiB in size or smaller), then maybe you're running into that 4GiB limit?

That's all I got. Probably not very helpful though...

P.S. Off topic but I recommend lighttpd (or nginx) as the web server instead of Apache - they're more light-weight webservers, so might be more preferable on an N900... though of course for your use case it may not matter. For lighttpd specifically, I have experience setting up PHP to be invoked by lighttpd through FCGI, and that was painless enough. (I suspect OwnCloud or Wordpress should work on top of any web server, unless they're tightly coupled to some specific Apache functionality, though admittedly you might find more tutorials/support for setting them up on top of Apache.)