Transparent is fairly quiet on design specifics but I'm almost positive they are not solid core.

It would be interesting to find my old post when I first got some BJC and compared them to IXO, Transparent, Radio Shack and Siltech. As memory serves we have similar observations, I found the BJC to be rolled off some on the high end, the Transparent to have better bass and extended top end, I can't remember if they were a tie on mids. I'm not sure which IXO I had but I hated it finding it to be very unbalanced with almost no bottom end to speak of. I found differences to be more apparent then you from what I read in to your post, however, I compared the cables using Sennheiser HD600's and a CDP into the Musical Fidelity X-can. Siltech was the clear winner but it was also the most expensive of the group I compared.

I know, cables can make a valuable improvement but rather than saying "you must" or "don't bother", I would tell any one interested to try for themselves and you make up your own mind whether you hear enough improvement to spend the money.