Nothing will fix the fact that ice is a terrible acoustic surface.
I'm not an audio engineer, but it seems like a straightforwards physics and geometry problem.
Create a large array of downward facing speakers, with narrow but slightly overlapping directional patterns, mounted above the ice, judges and audience, with sound-absorbing material (e.g., curtains and/or foam) around those speakers. Then the sound would bounce back upwards and be re-absorbed. It's such a simple solution, I don't get why it isn't used.
Bleachers, and the audience, where applicable, represent a more complex problem. Since they are above the plane of the ice surface (as are the judges), you need to produce the sound from those speakers with a timing delay. They and the audience also bounce part of the sound in other than vertical directions. Including into the walls of the rink, and the opposite wall of the building - which would have to absorb the sound, else you will get multiple sound bounces with time delays. Add to that the need for the top of the rink walls to be transparent, yet shatter resistant by hockey pucks, and they might be a more complex and expensive problem.
Nothing would be as good as a nice movie theater, but it could be a lot better than it is in some arenas.
Major sports arenas somehow solve most of the problem in other ways - but they throw a lot of money at it. A lot of ice rinks make little or no money, and can't afford fancy sound systems and qualified people to set them up. But it's hard to imagine being worse than the way some ice rinks do it - putting a single speaker on one side of the ice, sometimes right next to the judges. That gives you both time delays, and multiple sound bounces, to the worst possible degree.
The CD speed thing is easily solvable. If you use an adjustable speed CD, you accidentally might be off by 2 or 3 percent - up to about 5.4 seconds over a 3 minute program, 8.1 seconds over a 4.5 minute program. If you use one whose playback speed is electronically locked, that problem essentially disappears - a lot better than expecting each skater to shorten their program by that amount, just in case. OTOH, if the people who set up the test or comp don't understand the issue, they never think to solve it.