The other candidates would not get the remaining vote, the vote would simply go to the party without a name attached to it. This is because if every candidate were to get 1/7 of the vote you crossed out, you could take a list of 8, cross out 7 and all of these 7 votes would go to the remaining candidate on the list. The Swiss system does encourage expressing a preference for a candidate, but giving all of your votes to one candidate would create a unbalance, making it more difficult for new candidates to win a seat.
If you really want to only support one candidate and increase his or her chances of winning, then you'd have to cross out 7 of the 8 candidates, write down your preferred candidate's name a second time and leave all the other lines "blank". Therefore giving your candidate's party all of your 8 votes but not giving out the remaining 6 candidates' votes.
Also, you are right about how most media outlets do not publish the number of votes for each list. Which is why some election results end up being portrayed a bit misleadingly, encouraging the assumption that anything from 7'000 to 23'000 votes can get you into parliament (see Canton Basel-Town for instance). When in fact it's the percentage of party votes that really matters.
I found the following site to be very helpful (unfortunately most official websites do not offer extensive explanations in English).