Suggestions for higher efficiency speakers

Omega Loudspeakers will fit the bill and some come in nicely under your budget. Btw they are super musical 😊

I agree that Klipish and JBL are usually high efficient speakers. I would add ZU Audio to the list one can usually find them used on this site and other comparable sites. Two speakers in a cabinet and no crossover involved. PM me if you have specific questions.

Vintage Altecs (605, 604, Valencia, 19,...) are very high efficiency speakers.
You can find some of them on second hand market for less then $2K.
Klipsch Heresy also suite your requirements.
JBL are not  very high efficiency speakers but higher than average in term of sensitivity.

Regarding the Reference 3A MM de Capo, measurements of the BE version of that speaker performed by the National Research Council of Canada, as published by SoundStageNetwork.com, show a sensitivity of only 86.7 db.

Regards,
-- Al

I have Snell Type D at around 87 dB and Gallo 3.1 at around 88. Not exactly inefficient but could be better.

No- this is **exactly** what inefficient looks like (its at the upper end of inefficient- almost moderate). These are inappropriate speakers to use with an SET.

This is what you are up against: To get full bandwidth from an SET in general 7-8 watts is about the maximum before the difficulties of building a truly full-range output transformer begins to strain the idea of it being 'hifi'. Generally speaking this usually means you are limited to a 300b or the like for maximum power. Now of course there are higher powered SETs out there but usually the tradeoff is limited bass for more power because of the output transformer.
The next problem is that most SETs for good reasons don't employ feedback to minimize distortion. The result is two-fold: first this helps them have distortion at low power that is unmeasurable (the 'good reason' and the source of the 'inner detail' for which SETs are so well known). Second, distortion starts to take off at about 20-25% of full power. Initially the distortion is really only on transients which are common in music; since the ear uses higher ordered harmonics to sense sound pressure, the result is a 'dynamic' quality that other amps seem to lack. You really don't want to invoke this aspect of the amplifier! You simply won't be hearing everything it has to offer.
So the result is you need a really efficient speaker to take advantage of an SET. In smaller rooms this might be a minimum of 96-97dB 1 watt/1 meter, in a bigger room this might be 103dB minimum. And that is assuming you have 7 watts full power!