"By the way, I think the general consensus is that the LS-5 Mk II is better than Mk III?"
"Better" is always a tough term here as it provides little if any objective value.
There is one A'gon member (name escapes me) who prefers the II. But myself and two local (Minneapolis) previous owners of the LS5 disagree. In 1997, I went to my ARC dealer with my LS5 II to compare to the III. The III had a far more tonally coherent presentation. There was also more resolution in the mids and lower trebles with the III. The 3-dimensionality characteristics were otherwise identical. Had this not been the case, I would have eliminated the III from the running as this was what got me addicted to the LS5 in the first place back in 1995. I would have gone for the III but the $1500 upgrade cost was simply not a good value at the time. The amp used was a VT100. I do not remember the source or speakers.
When I took my II to a local audiophile's home to hear the III again, the same results: we both prefered the III. In time the II can be a little fatiguing due to an unnatural overshoot in the trebles. The amp then was also the VT100 driven my Theta DAC - speakers were Wilson WP. This system had phenomenol resolution and imaging.
And a few years later, another local audiophile who was selling a III, brought it to my home. Same results. After listening to the III, the II is tough to go back to because of the treble fatigue. The II however rendered a little more low-end extension/presence than the III. Whether or not this was accurate, who knows. Without being able to directly jump from one to the other in the same system, these differences would likely not be detected. The amp was the VT130 driving Magnepan 3.3.
He also brought over his LS15 and both LS5's smoked this instantly. The LS15 was eliminated in a matter of seconds for its dull portrayal of space and decays.
The one benefit of the II is that it has 30db of gain vs the III being configured as 12 or 18db. The latter requires a change of 8 resistors. If you use a phono source and your phono stage is not so high in gain, the extra gain of the II can be beneficial.
Hope this helps.