Are your speakers wired for 12 ohm or 6 ohm. Could be the reason the SET worked
The SE III's have a very flat curve at 10ohms and are 97db efficient at 10 ohms. It is as much the flatness of the response curve as it the sensitivity that contributes to their compatibility with SET, but there are certainly all kinds of reasons they do work well with SET. Simply being rated at "6 or 12 ohms" does not necessarily mean they'll work well with SET. I used mine with a pair 8 watt 300B based SET amps and they worked superbly in that application. The only aspect of performance I really missed was extension at both ends and that was more the amp than the speaker. The ss amp I'm currently using solved that, but at some expense to that holographic staging that SET is so good at.
I also sit nearfield - around 7-8 feet from the speakers which is the minimum Blume recommends for those speakers. I cannot think of another speaker they sound like in terms of a dynamic-driver speaker. They do remind me somewhat of the sound of a horn speaker in that way, but ultimately nothing but a horn sounds like a horn. Perhaps some of the Vienna Acoustics floorstanders have reminded me of the sound (Beethoven mini Grand), but my exposure there is pretty limited (only heard them at shows and have never owned them).
Hope that helps.