"I will follow your advice and order an inexpensive spare dial for fitting as well."
I use a low cost or no cost dial from a quartz watch or anything the right diameter and thickness (usually .4mm). A repair shop may have one or eBay for very little $$. You can mount a dial in a Dremel tool arbor like used for cut-off discs to spin the dial and sand it down to size if it is too big. You might have to enlarge the center hole to accept the arbor screw first.
"Will normal ETA hands work or do I need ones with a longer post?"
Regular DJ/tudor type hands to fit Eta 28xx should be fine. The hour and minute wheels on the movement should be tall enough to give sufficient hand distance from the dial and each other.
"I've read a lot about how adhesives can get soft and work their way into the movement when the watch heats up. Can you comment on that and perhaps recommend a tape that you have had good experiences with?"
I have used two part 'slow set' epoxy and clear Gorilla glue with good results...epoxy being slightly better of the two. Never had any trouble with epoxy or Gorilla glue 'crawling' away from where it was applied after it sets up.
Dial dots/dial strips can allow dials to crawl because the adhesive remains soft and some types will also bleed the adhesive away from where the dot/strip was applied. Dial dots and strips are handy for cheapo quartz projects, they work fine for things like that with light weight parts and no auto winding weight flopping around.