Removing the adhesive is one of those real go slow, hold your breath jobs.
I do a bit of work on mechanical watches and its not unlike cleaning up dials on mechanical watches - one false move and you're a letter or two down.
I used a wet toothpick for most of it. Start on the areas where theres's no printing - you can use pressure here as the wet wood won't scratch the glass. Then eventually you end up with just a little adhesive clinging to the actual days of the week in the middle of the glass.
Other tips I have for this bit are -
1/ Use a loupe and go around the letters first. This gets most of it. Don't be afraid to sharpen, point or 'wedge' your pick to get the right shape for a particular glob of adhesive.
2/ Go over the letters
where necessary in line with the lettering. Any pressure across the line of the printing is more likely to dislodge it than if you run up along the line of the print.
3/ KNOW WHEN TO STOP!!!! If there's a particualrly stubborn little glob then perhaps you should just leave it. Its hard to do this until you've ruined a couple of dials through being overzealous. I got everything off this one but was definitely into 'perhaps I should just leave it now territory before I had got it all..... For these Seiko glasses remember that you are cleaning the back side polariser. If you put a new self-adhesive polariser on the back side (recommended as they are about the right thickness and you won't have to 'shim' the stack to get your zebra strips lined up....) then a little bit of adhesive can be accomodated by the new film and at worst may just look like a feint shadow on the rear reflector in use. Similar little bits of old adhesive on the front will be obvious and at best cause the diaplay to blur.
I got the impression that the paint was pretty well stuck to the glass but you just don't know until a piece comes off. I've had beautiful mechanical dials shed lettering with not much more than looking at them so I'm perhaps overly cautious with this.
One cleaned off I
roll over it with a damp cotton bud a few times (means you can apply a little pressure without dragging accross the lettering) Dry cottonbud a few times to dry it off. Wipe and dab with Rodico. Then dry cotton bud to clear any remaining streaks. Blow for lint and then assemble.
Don't use any solvents on the thing. Clean water is fine.
Hold it only by the (long) outside edges that the contacts are printed next to - the short outside edges have hard seals on the glass-glass interface that if damaged will blead the LC.