I am not a lunarian, nor a lunatic although some may have referred to me thusly!
In terms of your intended observation, I personally do not see anything astronomically special. It may be auspicious and tickle your fancy to perform it during the eclipse. Your observation will be a star-moon lunar, in which some of the moon's light is attenuated by the eclipse. There are other methods which attenuate light, like filters. Am I missing something?
I've taken advantage of other oddities but in retrospect, the oddity is more like a novelty than anything unique or otherwise advantageous. This is the same thought I had when you originally posted, but held off.
There are a few lunar observations that could be pursued that do possess some degree of special nature. These may not have been performed historically for obvious reasons.
1) Accounting for the hills and valleys at the rim. Frank and I have briefly discussed this over the years. Frank could add it into his online solution but has yet to implement it. He says its something about making a living, and I do understand that. This has the singular attribute of improving lunars for all lunarians, not just a singular observation.
2) Lunars during an occultation. The 0° LD at observation is tricky in terms of timing.
3) Large angle lunars with the sun. Cook famously took lunars to ~155°. While that isn't possible with a sextant, a Circle of Reflection can measure angles well beyond 200°. I've tried a few of these large angle lunars and they are immensely difficult.
4) Lunars with Venus. As both objects have an appreciable disk, particularly under magnification, the reduction could prove tricky! Recent discussions about the Venus center of light have illuminated (pun fully intended) this thought.
Of course there may be others. Please do not take this as anywhere near an exhaustive list. This is just the opinion of one peanut gallery inhabitant, and your milage may vary.