Oh, and now my GPU's going at about 71-76C at the same settings (with 1-4 other people in the server) - is it possible that it might hit dangerous temperatures when I join servers that have lots of people in them?
You'll have to run a little test to see what level the temperature rises when you play for an hour or so on a busy server.
Some cards seems to be better able to withstand high temperatures than others, mainly those that come with passive cooling (IE: no fan). According to my Nvidia control panel the videocards won't shut down until they reach 130c... It is in no way recommended to play at a temperature that can boil water!
Anyhow, to answer your other questions;
Would extra cooling improve performance or reduce bluescreens, by any chance?
Yes and no. Mostly a blue screen means a conflict somewhere, not necessarily a heat problem. Although the conflict can be caused by a heat problem I suppose.
What overheating will mainly do is cause slow downs and artifacting. Sometimes even leading to a shutdown if the temperature reaches a critical level.
And would upgrading anything else reduce the heat load on the graphics card (e.g., power supply, motherboard, ram, and processor)?
Having a good airflow is a must but since all your other parts are quite well cooled I'd say your GPU might just need something more powerful to get the temperature down. The rest is apparently cooled well enough as far as we can tell from a screenshot.
Hope this helps. In the end, it's your decision. The cooler components run, the longer their life expectancy and the better their performance.