Its possible you could get a bit more power out of it, but not likely too much. I believe yours was bare to start with, and sounds like it was out of alignment from the get go from that power level. This is one of the hard to open sealed OEM heads, and its not going to have left the factory without good alignment for starters, so unless someone used it as a hammer, its not likely to have changed enough to matter.
Lazer isn't greatly knowledgeable on taking apart these heads either and trying to do so risks the tube, and for someone always asking me which end is the cathode, I dont think it'd be wise to try taking it apart. Plus, breakage aside, REO uses very thin metal mirror stems unlike the rigid wide MG ones, so every time you bend the mirror mount, you stretch it out and make it weaker, which eventually causes the mirror mounts to 'droop' and can no longer hold themselves rigid, which is a common problem on all REOs. REO heads are usually never perfect, and there's a margin of error acceptable. Plus, removing it from the head makes it unstable from even tiny drafts of air, and exposes it to continual HV and breakage dangers. The cylinder is put around the tube for a reason.
Also, think about the mirror structure. If its symmetrical, its unlikely to be out of alignment simply by nature of the reflective structure. Walking the mirrors instead may help a bit if not aligned with respect to the bore perhaps, but its already doing over its rated power, so its not really needed. If it was really out, it'd still be TEM00 due to limiting mirror access, or some other non-symmetrical mode (multiple beams from multiple reflections internally). TEM01* is basically just an expanded TEM00 because the mirrors are spaced too far apart, so it is resonating without the center. If spaced even further apart you'll actually get a dot in the middle of the torus. I know countless REO heads that behave this way, and actually even one of my HeCds is like this, being right on the verge between TEM00 and TEM01* (torus) due to the tube mirrors being ever so slightly too far apart by a hair's width-likely due to manufacturing error. So it's kinda like a shallow TEM00 with a weak center, almost TEM01* but not quite there. the reason the 604.6 is resonating in TEM01* is likely due to the extreme lack of gain in the medium as the 611.8 is hogging all of the gain medium. I'll never understand why REO uses an HR that isnt totally reflective on most of their tubes. but by carefully designing an external resonator with most of these you can do interesting things. I've actually made my LHYR-M do all the lines at once except green with extra mirrors, including a relatively strong and consistant emission at 609nm, rather than waiting for it to play on its own terms. :tinfoil:
Basically. If it ain't broke, dont try to fix it. I've broke more than one tube scrambling for that extra quarter milliwatt. It isn't worth it.