Do appeal it. I'm not sure how far you'd get but still worth doing.
Focus heavily on anything procedural - any unreasonable delays, anything at all that they didn't do right or well in terms of the actual process.
Also focus heavily on the fact that they allowed you to continue working, that's really important.
They've chickened out of sacking you all, presumably because of the inconvenience to them but also probably because they've taken advice and realised that they can't claim a breakdown in trust if they've allowed you to continue working. Obviously the argument would be stronger if they'd dismissed you, but you can still use it to illustrate that the warning level is unreasonably high.
If they thought it was fine for you to carry on working, they can't claim a breakdown in trust or anything like it, so your argument would be that suddenly imposing a final written warning is unreasonably harsh.
Obviously theft is a very serious thing, it is a sackable offence absolutely, and as we've established, it is actually perfectly legal to dismiss more than one person in circumstances where it is not possible to prove who was responsible. So a final written warning isn't actually bad. But as you didn't do it, it's obviously awful and you can and must use every argument you can to your advantage.
I personally don't think you'll get that level of warning reduced, because of the seriousness of the offence. Obviously you are innocent but someone isn't, and if they reduce the warning level for you they'll have to do it for everyone, which means that someone who is guilty of theft will only be on (for example) a first written warning, which may not be acceptable to them. But you never know, if you focus on procedure, their failure to suspend you and previous good character and service then you might get somewhere.
Best of luck with it. You could consider chucking a grievance at them as well, that would be perfectly valid if you want to do that. Again, not sure what it would actually get you though, so may not be worth it.