I assume you're working on a mythic given your request's requirements. To be honest, you don't need a linkshell to do any of this(einherjar would be made quite a bit easier with a full ls but it's not a requirement) and chances are you wouldn't find one that would do all of this anyway as the game is much more lowman focused than before. What you need is:
Do shouts for salvage, if you only want the clear offer all the gear as free lot, hell, most jobs can solo salvage or find a friend and duo the runs. This portion for a mythic is simply getting the clear titles which is very easy. 5 wins and you're done, no ls needed.
Assault is something I'd recommend getting a set for. It might be somewhat difficult to find one considering most people are putting all their tags in to neo-nyzul. While you could likely do very nearly all the assaults with 3 people, I'd recommend more for a few of them as they are rather luck based or hard to do with less. Again, an LS isn't really going to help here as you don't need a big ls to do this, you just need a small group of friends with similar goals or are willing to help out. You can try shouting for it or just posting specifically looking for a set and try to find people who will work out.
Old nyzul is incredibly easy now, though I'd recommend getting some good experience with it as you'll need that knowledge for neo. Probably another good set event since you only need 3-6 people for it. If you have more then you are very likely to be able to clear a good 10 floors even if you are inexperienced. I recommend educating yourself on the event first, read up and see if you can get some friends to help you try a run so you know what to do. Again, since this takes tags, it may be harder to find a set but there are people out there who need it, you just need to find em.
Einherjar is probably the closest thing to needing an LS out of all of these but really, you can just join shout groups. There are tons of people making mythics who lack the points they need so find them and go along, it's probably not too hard to find a group, if you need to search the zone occasionally and see if they are willing to let you tag along when they go.
Good luck.