Not having heard any of the preamps you are considering, I haven't a clue. But, as an aside, all 3 are preamps I have been reading about for a several months and are curious about myself.

The BAT supposedly has an upper midrange prominence that if true would nix it for me and wouldn't appear to address your desire for 'sweetness.'

For a long time, the Audible Illusions Modulus 3A was on my shortlist. A friend warned against some midrange glare in an earlier incarnation. The phono stage always seemed like a plus in my book. I'm unfamiliar with the other two, and it's been ages since I've heard the AI. Is there a way for you to check out all three in the same system for a level playing field?

Yes, the Audible Illusions, for "sweetness." It makes less-than-perfect software (merely about 90-95 percent of your collection) sound sweet and silky. It will take out some extreme definition from your perfectly recorded sources, but they won't be much the worse for it. I sold mine 3 years ago and will probably buy one again. It images like a champ. Huge soundstage. For the money, I don't see how you can beat this piece, if you are into tubes -- the "gold" phono section is the way to go, unless you use higher output pickups. I still prefer an outboard phono preamp, for flexibility reasons. True, they are more expensive than the $500 or so extra you pay for the Audible Illusions "Gold," but some of the newer ones in the $2000 to $3000 range are so quiet and versatile that it is worth the extra bucks for me. Jeff, there is no glare on the models after around 1997 or thereabouts. This is a very neutral preamp that has gotten some unmerited bad rumor-press. You know the drill. People hear rumors, and they like to display their golden ears by jumpin' on the pile. This is a classic piece of gear and value priced. Cheers and happy listening, Clifton.

I have to admit something.Something that will drive everyone here nuts.I never listened to a single component before purchasing.I am not going to go into details here about how i choose what to purchase (it would take pages).
I suppose you want tubes in your pre amplifier. Well,from what i know,i'd go for the VTL. If tubes are not a must then i'd consider something from Jeff Rowland.

I've had an Audible Illusions pre amp for over fifteen years and find it hard to beat at a price I can afford. However, if you are searching for a bit more "sweetness", look for a pre amp with 12AX7's or one of the 12A- variations. The AI uses 6DJ8's and became known primarily for the geting away from the sweetness of the ubiquitous 12AX7 pre amps. I went from a Marantz 7C and a Conrad Johnson PV-5 to the Modulus and the difference through the mids could hardly be more striking. Any tube pre amp with the 12 series tubes will have the same midrange quality but the AX7 has become the tube of choice in pre amps for the quality of sound you seem to want. Alternatively, you can take a Modulus and rewire the tube sockets for 12AX7's. This gains you the dual mono design but gives up much of what makes the Modulus a cult pre amp of choice. If you have the cash and really want the sweetness without the frequency extremes being problematic, I would go for a reissue McIntosh C22.

Not a reissue but who's keeping score? This is a classic.
http://www.audioclassics.com/cat.php3?cat=Preamplifiers&p=0

Audiogon doesn't have a reissue either but it's a good place to watch.
http://buy0.audiogon.com/cgia/fsb.pl?preatube&1&ctg&st151

I had a BAT3i and 5i and liked both for the remote control and general capability - no real weaknesses. However I now have a Tron Comet (current model: Syren) which is definitely superior and should be on your shortlist; also has excellent phono. Not sure what the US price is, certainly in Sterling it's comparable.

website is www.tron-electric.co.uk
review on 6moons - http://www.6moons.com/audioreviews/tron/syren.html