I can't offer any advice that pertains to Eureka, but perhaps I can offer a friendly word or two when it comes to grouping with others.
I think you probably should ask yourself why you avoid grouping with others, especially when the FFXIV community is one of the friendliest in the mmo genre. There's no need for a guide when other players will be willing to help you, but you have to ask; they're not just going to land on your lap. I know you said you don't want to be a hinderance to others, but this is self-defeating. With this mentality, you are only hindering your own progress. I saw your thread last night asking for a raise, but if you had a healer buddy with you just imagine how much more convenient it would be for the both of you: They have you to add to DPS so things die faster, and they can raise you on the spot should the unfortunate happen, and I would imagine no one gets through all of Eureka without getting KO'd here and there.
I don't think it's just feeling like you'll only be trouble for others, because I can tell you are fully aware that grouping with others speeds up progress. I believe some social anxiety is also at play here. It's ok, and I fully relate. The game does cater a lot for the solo-minded player. We're even getting trust NPCs next expansion to help players progress through content, much to my chagrin. But SE also encourages grouping, and things will always be more efficient when you do so - well, most of the time lol.
I know it can be tough mudding through those uncomfortable feelings, but trust me when I say that players can and will be willing to help you out. You just need to make it known that you're new, unfamiliar, a returning player, etc. This deflates a lot of that tension you will sense otherwise. You're also not alone. There's going to be players much like yourself in there as well. Try your best to push past and not only you will get stuff done faster, you will also have a lot more fun in the process.
I wish you the best of luck!