So for your scenario, least expensive, and best option I see is training your video crew to do on hill editing by handling the skiers/communication better.
What you need for this scenario is:
2 radio's one with an ear bud would work best.
2 people. One somewhere on the course with a good view of the whole course. One to handle the camera.
Mark a section of the course in the middle somewhere (start and stop)
example would be if the course is 30 gates, plan on recording gates 10-20. (or a specific technical part of the course (ie you want to see how they handle a fall-away pace changing section)
The video person would situate them self somewhere where they can get a good view of the whole section to be recorded. Make sure the start section is brightly and clearly marked so the video person can use it to find the racer and pick them up as they enter the "recorded section" The video capture should be stopped and restarted between each racer. Best scenario for location is if the video person is practiced enough, they would stand somewhere around gate 15 (off to the side enough so they don't have to zoom in and out as much when the skier passes) and get several gates coming and several gates going.. I say "practiced" as this is a skill not easily mastered. You have to keep the person in your view and zoom out and back in as they pass. Then you have to re-acquire your next target quickly as the enter the recording area, while stopping and starting the recording. Second best scenario is well below the recorded area so you can zoom back into the start location as soon as they leave the recording area
The spotter or second person ideally would be at the top or be able to radio to the top, when to start the next racer so that after the first racer leaves the recording area, the next skier will be starting through the first few gates and building their rhythm. Timing should be such that as or after the skier leaves the recording section, the video person would have enough time to stop the camera, re focus attention on the start location for the next skier and capture them as they enter the recording area.
The spotter should continually update the video person where the next person to capture is on the course. Just in case you have a real slow skier in the middle. You may have to either give up on a few last turns early to capture the next person, or give up the first few turns to allow the first skier to complete their section. This where real practice comes in. If you have to acquire a moving target after they have passed the "brightly marked" start spot, it gets harder.
The other logistics part is making sure you know what order they came down in or use Jerseys' or numbered jackets/vests
Using a scenario like this would give you a series of video clips that could just be uploaded to your host of choice without editing.. The better the recording, the better the result will be.
If you know you have 25 racers and you end up with 25 clips, hopefully the racers and their coaches will know what order they came down in and should be able to find themselves in the group based on time stamps and order of recording.