Most Honda's do this, it's pretty normal. I feel other ill effects too, if I turn my lights and/or defroster on, it's enough of a draw that I can feel a definite hit in power in 1st...car needs more gas to get it going.
Since it is caused by the ELD unit, I think you have a couple choices. 1) Disable the ELD unit and make the alternator run all the time - not sure how you would do this but suggest you don't If you disable it, you will take a hit on fuel economy, void your warranty, you can't guarantee whether the alternator is going to stick in high or low output mode, possibly make the alternator wear out abnormally fast, etc. 2) You buy a bigger/better battery and hope for the best. I am not quite sure if this will help either, but your best bet would be to ask someone who got a nice battery (like greg-ster and his Optima) to see if it made any difference for them. My thought is that since this dimming is caused by the ELD switching the alternator from low to high output mode, if the battery can compensate for the current disparity, even for a split second, then your case should be helped somewhat but might not be completely eliminated. Anyone else have insight on this, whether I'm right or is there something about the system I missed that would make the new battery have no effect?