I'm a bit surprised no one has replied by now . . . well it is Friday! So here's my 2¢

Sounds like either your undo retention period is unreasonably long or you have badly understimated the cost of flashback. You'll have to review this or the problem will just repeat itself.

As you've got other disk, you could move some datafiles there so that your users can continue to work, while you sort it out properly. (This is Urgent.)

My preference is to do a cold backup as part of this:
1. shutdown
2. backup
3. move datafile(s) to other disk
4. startup mount
5. alter tablespace rename datafile 'AAA' to 'ZZZ'
6. open

You could chose to move the undo . . . .

There are more elegant ways without a shutdown (putting TS offline etc etc). I'm hyper-cautious (it comes with old age) I prefer the above.