Okay, first of all, it turns out I was using an old version of Wine. It was actually when I re-read my post that I realized that
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. I think I'd tried to do this a couple of times before, and my helper app that lets me launch Windows apps in Wine with a double-click was finding one of those older versions, which IIRC were directly from the Wine project. So I removed the older versions and fixed things to use the newer version I downloaded (1.0.1 stable). Since this version is set up with freetype, text looks *far* nicer, in some cases nicer than natively under Windows. And, most of the things that were sluggish are now a lot faster - except autocompletion menus :-/.
As a test, I tried installing Wine 1.1.21 (unstable), and it performs exactly the same with the autocompletion menus.
But then I had an idea. Noticing a lot of redraw activity elsewhere in the PhpED window while it was working on the autocompletion menu, I tried making the window smaller - and viola, reasonably fast autocomplete menus! When the window takes up most of the 1600x1200 screen, it's slow, but when I make the window closer to, say, 800x600, it works fast. Do you notice a change in draw speed between different window sizes? Any ideas on what I can do to speed things up at larger sizes?
FWIW, I have an NVIDIA GeForce 7300 GT graphics card.