Thanks, all of you for your responses; they've been helpful but I jumped the gun a bit. To have speakers in the system while I'm trying to decide what to do about the Odysseys, I ordered a used pair of Monitor Audio Silver eights from eBay. They actually sounded quite good in the showroom.
Going back to what I said earlier though, speakers that incorporated ribbon tweeters sounded best to me but, based on what I am reminded of on this forum, it could be for reasons not necessarily related to speaker construction. I say this because, in the store, the silver series Monitor Audio speakers are in a demo area where an A/V receiver with a speaker switching device is used to demonstrate speakers. On the other hand, the speakers with the ribbons are demonstrated in another room using more expensive separates with direct connections between the speakers done manually.
Anyway, it crossed my mind that, if one is very satisfied with a speaker except for the HF harshness, how reasonable might it be to consider replacement of its domed tweeter with a ribbon tweeter? I know that the considerations are many, the most obvious being redesign of crossover frequency points and slopes and physical modification of the cabinet to accommodate the different shape and size tweeter frame.
This may seem an outrageous concept but in my very early years I did do some of my own cabinet and x-over design and construction but that goes back to my youth when sound systems were monaural and relatively unsophisticated. Because I've been retired for a long time, though, my monetary resources are more limited than in the past but I do have more time to devote to interesting projects.
I know this sounds like little more than mental calisthenics but I really do want some input on this. I can no longer justify spending a lot of money on audio components but I haven't lost any desire for quality sound.
Current components are Shanling solid state CD player, CAL DAC, Rogue Audio 100W Sphinx hybrid stereo amp and 10 year old ML Odyssey speakers, one needing a power supply circuit board. These speakers will probably be sold after I install a new board.