I've never had a lot of problems with assassins, except in one specific run where I took a decision that I knew was going to make a lot of people very, very angry at Zorana, and my general angle is generally Zorana Being Nice, so I don't know how much I can help, but:
- on the whole sticking to the left half of the mood wheel seemingly is less deadly
- Empathy/Etiquette can be enough to avoid assassination attempts on the left half, I definitely find Rhetoric very helpful when it comes to making a good impression.
- Physical skills - Condition and Body Control - I tend to consider as defensive skills against right half assassination attempts of the mood wheel. You usually need another skill (Layout, or Guns), but if they're sufficiently high you can make it through
- just reiterating what was said by previous people, visiting Korundi can put you in Cautious, which is generally but not always safer, and the snake puts you in the safer half of the mood wheel as well.
- there's a few choices Zorana can make during the game that are offensive to some group or that some people will interpret as Zorana not caring for them. If Zorana shows lack of care for the same group a lot, then it'll be easier to pick up Electors from people who don't belong to that group, but that group might easily go from merely disliking Zorana to actively wanting her dead. Conversely, trying to balance out favor/disfavor means assassination attempts are less likely, but Electors might be less easy to pick up.
Personally I've found that what works best for me in the early game is getting a skilled cabinet from the Tharkan system and largely considering Myrkka II a wash. As far as I know you can't talk to the rival guy! He's not interested in being chummy with Zorana. There's a trick to getting the admiral on board that I use a lot (you need a little Piloting and a lot of aplomb) which I find cost-effective but I don't know if it makes a lot of difference Elector-wise.
Do you do a lot of retrying from the start of the turn/the previous turn? I've found that a number of assassinations are easy to survive or avoid if you go back only or or two turns - if there's an assassination attempt in Compliant on turn 16, you could go to Social on turn 15 so on turn 16 you can only pick between Indulgent and Excited, and sometimes assassination attempts can be survived with an emergency double work session in a key skill. I did a lot of reloading in that playthrough I was facing assassins all the time.