As Heatmizer says, the LM337 is the hottest part on the board, by far.
I agree with Eric's assessment of the tube and its affects on the sound. The opamp is close to the rest of it. The coupling caps have an affect somewhere close to or less than the opamp, but you can't roll them very well. Whereas, the tube and opamp are plug and un-plug. There are many reviews of various 12AU7 types for the SOHA - I've written a couple, in fact. Just search for SOHA tube reviews here and on Headwize. Tube rolling is great fun in the standard SOHA and the differences are great, maybe even extreme sometimes.
Good ones that are worth trying (I limited myself to <$20.00 tubes):
NOS:
GE 5963 (my and many other's favorite), big soundstage, does everything good - lots of detail. At one time, was as cheap as $4 at many tube dealers. Comes closest to operating at the SOHA's plate voltage. The SOHA biases at 40V, but the GE 5963 uses only 70V. That's another reason it's often cheap - it can't stand the plate voltage in many typical 12AU7 amps (100V).
GE 6680 Best highs - really extended, liquid and sweet
Raytheon CK5814A - Very nice, outstanding tube construction and it sounds like it.
Sylvania Gold Brand GB-5814A - very similar to the Raytheon above.
NEW:
ElectroHarmonix 12AU7 - very powerful tube, takes forever to break-in, but worth it - powerful bass with steely highs
JJ ECC82 - pretty much the standard tube for many, it does everything very well, very dependable.
As Eric states, there is no guarantee that a supposedly "boutique" 12AU7 type will sound good in the SOHA. As mentioned up there with the comments on the GE 5963 - the SOHA's plate voltage is 40VDC, whereas the normal plate voltage for a 12AU7 is 100V. That means they'll all sound different than what they're supposed to.
As for the output stage - short of the JISBOS, your best bet is to find an OPA2107 - that has worked the best for me and several others. Similar to the OPA627, it's often rejected in other amps because of a rather high voltage requirement. That's not an issue in the SOHA. Another good option is two OPA551's on a Brown Dog adapter. Either one of those combinations is a definite improvement over the OPA2134.
Of course, my own bias for a particular tube hybrid is well known around here (
MAX).
Still, the SOHA is a lot of fun at a low cost. As with most DIY amps, it will probably best many similar commercial amps costing 3-4 times as much.