Thanks for the helpful replies. Based on this advice, I decided to have my LaCie repaired locally by a television repair shop. I couldn’t find anyone within a couple hundred miles that repairs CRT monitors. My TV repair shop said that they can repair the most serious problem, where occasionally the screen goes blank except for a very thin, very bright white line horizontally across the center of the screen. They can’t do anything about the inability of my monitor to use high resolution and refresh rates, however.
So, for about $100, I’m hopeful that my LaCie will be usable again. I think $100 is a good investment, but it would not be worth much more, which precluded shipping my monitor to another repair facility.
If it turns out that my LaCie isn’t repaired adequately, or when it dies, then I’ll investigate recommendations for a replacement. The NEC xx90 series of monitors appears to be a very good place to start.
Once again, thank you for the helpful advice.