All the advice on this site insists if you're going to do this, do it early...if we arrive in Hawaii from the East Coast in the late afternoon/early evening, experience suggests (we visited Hawaii 15 years ago) it is likely we'll be awake early our first morning. We're staying at the Sheraton Waikiki. Would it be reasonable to plan to take a taxi over to Diamond Head just as soon as we're up? Would love advice about this.

We just did this a couple weeks ago. We arrived in the late afternoon, and went up to Diamond Head early the next morning. We came from the west coast though. Anyway, definitely go early. On our way down there were many more people just heading up and we were glad it wasn't that crowded for us.

Here's what Fodor's has to say:
http://tinyurl.com/3lu3gn

Yes.

We actually climbed Diamond Head late in the day when we were in Honolulu in September 2007. We were exiting the park just as it was closing. We didn't find the hiking or viewing platforms to be that crowded.

If the day you climb Diamond Head is a Saturday, you get a bonus. After you are done with the hike, head over to the Farmer's Market nearby to check out the local products Hawaii has to offer:

http://www.hfbf.org/FarmersMarketKCC.html

The market opens at 7:30, at which time you can get coffee and a local breakfast by a local chef using local products.

p.s. yes, definitely go early. All the advice on this site insists that, because it's true.