hmmm...turning into a politcal thread? not sure why, anyway, getting back to Edge:
No need to be a closet U2 fan, there are millions of us

. You may find some info on this on specific U2 forums (like interference
http://forum.interference.com/f259.html)
I've got to admit that most guitarists on those kinds of forums are not in the same league as jemsite when it comes to GAS. Many of the options discussed would fall in at the low end of gear, nothing wrong with a cheap solution, but it would only get you to about 50% of what is possible.
If you look at some of U2's videos you will see Edge's most famous guitars in action. He tends to use most of those in the studio as well as live, IIRC:
R!ckenbacker 6string (slide in Mysterious ways)
assortment of Str@ts ("blackie" in New Year's Day)
L&s Paul (cream colored LP Custom in the Fly, customized "Mirror ball" LP in Discotheque)
Explorer (70s reissue, I will follow)
assortment of semi hollowbodied ES335 type guitars.
List from interference:
-> '67 Fireglo Rickenbacker 330-12
-> '66 Cream
Fender Telecaster
-> '66 Lake Placid Blue Fender Telecaster
-> '66 Maple Rickenbacker 330-12
-> '62 Epiphone Sunburst Casino
-> '63 Gretsch 6122 Walnut Country Gentleman
-> '65 Gibson Pelham Blue SG
-> '75 Gibson Cream Les Paul Std with Custom Bridge Pickup
-> '73 Fender Black Strat with Custom Bridge Pickup
-> '76 Gibson Natural Explorer
-> '62 Fender Sunburst Strat with Custom Bridge Pickup
-> '61 Gibson Sunburst ES-335TD
-> '?? Gibson blonde 'Pete Townshend" J-200 Acoustic w. Fishman Bridge Transducer
-> Two custom Line 6 Variax Acoustic Guitars
check
http://forum.interference.com/t136075.html for more
I think he has some kind of deal with Fernandez (sustainer
http://www.fernandesguitars.com/menu.htm and he used to be with Hiwatt
http://www.hiwatt.com/) as well as Line6
http://www.line6.com/artists/202 but does't limit himself to their gear.
His early delay sound is an
Electro Harmonix Memory Man
Later he swithed to the above mentioned Korg (I think Vai used them too in those days)
For Achtung Baby, the edge used a Korg A1. I have a Digitech GSP2101 which does about everything the A1 does plus it includes a twintube preamp section. Delays go from 1ms to 5sec (10s with Dual Processor) everything is completely transparent (24/48bit) programmable, loopable, linkable, controllable incl continous controller. Look for either one used, but not many people will want to part with them. They're that good!
The successor to the GSP2101 is a floor mounted GNX unit (
http://www.digitech.com/products/gnx4.htm)
You may also want to check out the awesome Boss GT-Pro (
http://www.bosscorp.co.jp/products/en/GT-Pro/demos.html) both are both are 800-900 US$, I think.
You are right in looking for a unit programmable to the millisecond, the trick in Edge's sound is locking a delay with the tempo, a tap delay may work, but not for a live show. You need to be able to make as many presets as you have songs in your setlist. A pedal won't let you do that, even some rack units are limited. This is one of the reasons why Edge uses this custom thing
http://www.line6.com/news/general/122