Missions & Complexes

The calculation of standings within a player corporation uses raw standings of the individual players, so the connections skill won't help.

If your player corporation has a + 8 standing towards a specific NPC corporation (which also has stations with a medical facility), then everyone in the player corporation can install jump clones at that NPC corporation. Your post refers to faction standing, I
don't know if that works like that. (in the past it did for pos anchoring)

But the bigger problem if it really is faction standing, is that any member in the corporation (more than 7 days) who has any standing towards the same faction will drag the player corporation's standings down, which pretty much rules out anyone who has even done the tutorial career missions.

If it is really standing towards a specific NPC corporation (more usual), then to keep the jump clone eligibility for the entire player corporation, you don't want any of the other members to run missions for that NPC corp, otherwise they drag down the average standing.

I believe you have to be a member of the player corporation for 7 days before that player's standings affect the corp standings.
Before ccp changed the requirement for anchoring high sec POS's, that was usually one reason members would pop in and out of corporations.

And to get to 8.0, yes you have to grind missions, or time it to get one of that corp's storyline mission agents, or if you are lucky, hope that one of their agents is in the cosmos series and sells standings for tags (but you probably need a somewhat less popular or uncommonly used NPC corporation to keep the other members from fraternizing with that corporation)