First, I was able to knock a post with low numbers of votes off of your trending page just by voting for it with a small value

Yes, I've already done that to see how the score changes after a second (small) vote :-)
However, the influence is only apparent and only due to the fact that I recently changed the trending score calculation and that the recalculation only happens when the post or its votes have been changed.
The goal we wanted to achieve with the last change, to weaken the median with fewer votes, is thus achieved. Unfortunately, we won't be able to see for a few days whether it is really effective in comparison with other posts.

does this mean that if 10 web sites all run condenser and hivemind, they can use 10 different customized trending algorithms in order to distinguish themselves?

Basically yes.
Hivemind provides the trending score for the Steemit condenser. If other frontends also use the Hivemind data, they receive the same score.
There is also a calculation directly in BC Code in tags_api).
Frontend/Backend developers could also use other algorithms. For example, Steemchiller has its own trendings:

• https://sds0.steemworld.org/describeMethod/feeds_api.getActivePostsByTrending
• https://sds0.steemworld.org/describeMethod/feeds_api.getActivePostsByTrendingWithoutWhales