Most Engaging Monitor?

what is musical to someone can be too subjective.
There are lots of dependency out there all the way from the source -> cd player or vinyl -> cables -> preamp -> amp -> cables -> spkrs -> ears. Anything mismatched can sound bad while any matched good sound great.
one should ask:
high freq response:
mid range response:
Low freq response:
sound stage:
placement:
room size:

so back to your question:... my answer would be it dpends..
what amp are you using to drive?
what spk and interconnect are you using?
what stand are you using.
I personally prefer professional studio monitors as they are more engaging and accurate to me.

Before shooting in the dark, please try to audition and purchase from someone local and deal with it face to face.

interesting thing about the LS3/5a I read recently that the older models have a smooth rise of about 3 db in the 1000 hz range (if my memory serves me correctly) I am not talking about the built in bump at 125 hz, this is something that happens over time when the speaker is several years old. Not that every speaker out does not have this bump, I thought it was interesting about the LS3/5a...

Price wise, used JMR Twins are great at around $5-600. I haven't seen any used Dulcets in a while. The Harbeths would be the most expensive as would the classic Rogers LS3/5a. Placement would also be an issue. Sealed cabinet or front ported would allow me to use the speakers closer to the wall.

The original Rogers LS3/5a was the first speaker I heard that shook my world and made my ears realize what real reproduced music really should sound like. This was in 1977 when I first heard these speakers driven by Audio Research electronics and a fine-tuned turntable with a Koetsu cartridge. My life has never been the same since. Here is an interesting site dedicated to this remarkable speaker:

http://www.ls35a.com/

why not consider a pair of 16 ohm rogers ls 3/5a ?

Of the three you picked, I have owned the JM twins and Ref.3a Dulcet. I currently still own and enjoy the Dulcet. IMHO, it is much more musically accurate than the JM speakers. I also owned a larger version of the Harbeths, the 7ES, and the tiny Dulcet speakers rule. There's something special about time and phase accurate speakers.

JM Reynaud would be my choice, however I would recommend the Trentes that are available here on Agon...

All are good choices but I really like the Reynaud for an all nighter.

good luck and enjoy