I'd try figuring out which flashpoints give companion influence, and which other quests you can do that make the companions happy.
The thing that really bothers me about 4.0 is the older players/companions really do not have a competitive way to level up their influence as we've already completed a lot of, if not all of, our companion's conversations. They did nothing to retroactively give those companions an average boost to their influence or do anything to help us since we will not be able to naturally level them through story progression.
Through story progression I have a trooper that is sitting on an influence level 24 or so companion - she didn't gift that companion at all, but I have level 60+ that are running with level 10 companions because there was no influence conversion for those older characters so I'm now stuck having to gift them up.
That all said, I do have all but one of the class perks and I am sitting at 498 bonus presence at level 65. I have all datacrons and the race bonuses figured into that.
I was able to solo heroics on an instant 60 with an influence level 1 companion, but it was a horrible struggle and not one I would ever want to repeat. It was doable, the first two had me thinking it was great, me not having too many issues must have meant the scaling would make up for it, the companion nerf wasn't that bad. After the 3rd I didn't want to hit the 4th, I was playing carefully and trying not to over aggro etc. For a new player or someone without all the buffs I have it's going to be a struggle for a lot of things till they find a happy medium for the nerf/buffs.
