I did something dumb - password reset help (14.2 x64)

I set-up Slackware64 14.2 multilib on a machine a few weeks ago, and then set the machine aside while dealing with other projects, and now I cannot remember either the user password or the root password for the box (and yes I've done the 'spend 2 days throwing everything I can think of at it' routine). I know with Ubuntu and other GRUB-based distros you can get a 'recovery' mode on start-up and run single-user, re-mount the file system, and change the root/superuser password that way (and then from there change all the lower user passwords one by one or force them all to be reset by users), but I'm not seeing how that works with LILO/Slackware intuitively. Any 'easy' solutions to this would be appreciated (as in, something as simple and non-destructive as the aforesaid), otherwise she's getting nuked from orbit and doing a fresh install of whateverOS.

I also did try to search on LQ and it just keeps returning 'Database error' so apologies if this is a very commonly asked-and-answered question.