I don't think I have ever heard the ICE amps, but have definitely heard my share of digital amps. Most enjoyable of the bunch were the Channel Islands amps. They don't look like much and they are simply designed, but the sound was excellent. However, I would not classify the sound as analog like. It is actually hard to describe although it was pleasing to me. Rick at EVS is supposed to have some new amps that are outstanding as well.
Dazzdax - if you really want that analog sound from your amp you need to listen to the solid state TRL D-225 or ST-225 integrated. I have had the D-225 in my system for about 6 months now and it is trul amazing. I am now using it primarily with a passive preamp (although I am contemplating the TRL battery powered preamp) and it is amazing how much more analog the sound is versus my older tube set-up. These amps aren't much on looks, especially versus Accuphase, but they have the sound you desire. Cost wise, they are not in the same league as most of the ICE/digital amps, but they are an excellent value nontheless. You should give Paul Weitzel a call. Money back guarantee as well.