I thought about that, but given the level of my dexterity with stuff like this I thought I'd see if I just missed it some where.
It doesn't take much dex to do - anything that can position and hold the battery in place against the contacts will do.
Some years ago, I bought a charger for "loose" lithium cells and it's made with a clamp that presses the battery onto the rest of the (wall wart like) charger and two moveable arms carry the contacts - I use it for phone and cam batteries and the like when I haven't got the proper charger, or the phone/whatever it belongs to. The two plastic+contact arms simply swings in an arc to adjust the center distance and then you jam the cell against the contacts and release the clamp.
Using matrix board for holding a couple of contacts, you could solder or glue small strips of PCB or plastic to form a rectangle - as long as it will hit the contacts (which you could always bend a bit) and stay in contact,it will work. a few strips of self adhesive window seal or similar may help it from sliding if the "frame" get's a little too large.
Would I need some kind of interface circuit for this to manage discharge, etc? Or can I just run + and - from the battery?
You need to detect (and stop discharging at) a suitable lower voltage, eg. 3.0V, but apart from that, it's plain sailing.
You'll need a charger made for it as well, unless you want to use a phone for that (or if you have one of the Nokia charging stands that takes an extra battery, that could be used).
Should it ever go below ~2.5-2.8V, use a low charge current until it reaches 3.0V
My GF got an SE Experia X10 Mini Pro from a friend, as he went with an iPhone. It had been lying in his drawer for around half a year and the battery was reading 0.00V
, so I wasn't too optimistic, but on the other hand, you cannot kill a dead battery and by hand charging it with a lab supply (and some caution), I managed to necromance it to take a charge and while its age (a couple of years and down to around 70..80% of a new battery) shows, she's been using it every day for around a little over a month (and she plays games on it and fiddle with it a lot).
Only goes to show that all the voices who claims it impossible saving a cell that has gone under 2-point-something volts are just repeating what they read somewhere, without having neither any practical experience, nor a functional filter to sort the few percent of truth from all the rubbish that is floating around the web these days.