Curiosity question--are you running any SB themes? I used to see a similar bug on occasion clear back on 4.3.3 with my iPad; took me a while to track it down to some weird SB widget that didn't play well with the calendar for reasons I never precisely figured out. It drove me nuts for quite a while. IIRC, the widget had a non standard way of calculating the date; ended up having to redo it to the more common HTML coding and the problem disappeared after that.
Unfortunately, I've not seen this happen even though I'm on a 5 with 6.1 and all current evasi0n updates as well, so I can't help with troubleshooting this one. (I'm with you on not bothering to update iOS for the small stuff, so I didn't bother with 6.1.2.) Hopefully someone who had your actual problem recently has found a solution! But, assuming there's no actual fix to be found and you want to use the stock app, about the only alternative I can think of would be to use a plist in Winterboard to "hide" the date that appears on the icon--changing the icon itself will have no effect on the date. A plist will able to change the numerical text to white to hide on the stock icon background. Or you can also use one to make the text fully transparent, so you wouldn't have to change it every time you changed icon themes. If you're not sure what I'm saying, LMK and I'll see if I can post an exact one for you to use.
Obviously, it's a less than ideal solution, because it just hides the problem. But if you're the type who runs a date widget on your phone anyway, it might be an OK thing, at least while you continue to hunt for a better alternative.
(Note--if you go the plist route for transparency , do NOT use "display:none;" but rather "opacity:0.0;" The former will throw you into Safe Mode & keep you there until you delete that from your plist. The latter produces a blank field where the number used to show, as pictured.)