You cannot Expand (or in your case, Invade) unless you're at 75% Influence. You pretty much have to take control of the system to get there; while it is possible to reach the 75% influence level without controlling the system, it's really hard to do.
Wolf 359 is not Red Squadron's home system; Luyten's Star is. Far fewer people care about what happens in Luyten's Star, compared to Wolf 359. It is a Sirius Corp system, so you'll always have some passing traffic wanting to level up with Sirius Corp to get the permit for Qwent, unless you and your friends put in a concerted effort to get Sirius Corp completely evicted from the system. But it will probably be easier getting a takeover and expansion happening from there, than from Wolf 359.
The trouble then becomes, where would you expand to, that isn't also hotly contested property. Being so close to Sol, all the systems are already full, so you'd be likely running an Invasion rather than a regular Expansion. Duamta is probably the closest Invasion target to Luyten's Star, and it's also hotly contested, huge population with a native PMF owning half the stations and the dominant NPC Fed faction the other half.
if not for all the new negative effects, we would have been in investment a few times by now and had an easier time increasing influence so we could expand out of the system
Investment doesn't really help you to expand. Prior to the 3.3 States reworking, "Investment" was what happened when a faction tried to Expand, but literally had nowhere to go; they were already present in every single possible destination system. Investment made the next Expansion sphere larger, to hopefully include more systems to expand into. But the only places I ever saw Investment were in isolated, remote outposts, where there was nowhere to expand into for hundreds of LY so it never really worked as intended.
Now, Investment just means "extra-good economy", the level above Boom. It creates different kinds of missions, but otherwise has no impact in the ability to gain influence and thus expand.