If one knows/learns how to "game the System", progress towards Grade 5 access for any Engineer is done fairly quickly.
Unlocking them can be a different story, however, and no matter how I put it... that always just felt like a limited Grind. Just gotta do it and bunny-hop through the mandatory grind gates. No way around them.
You get the Invitation and it basically states "You're welcome and invited to my place, looking forward to meet you. But I'll refuse to do anything for you beyond docking permission or refuel. Bring tons of goodies and I'll reconsider."
(go ahead and send such a type of "invitation" to your friends and see how many actually turn up

)
Anyway, "gaming the System" after unlocking an Engineer (initial Grade 1 access) :
- gather alot of Grade 1 Elements (Iron, Nickel, Sulphur, Phosphorous, Carbon), those are easy to get on Planets / any dedicated Miner is likely also full of these already
- at Engineer, spam Grade 1 Upgrades until Grade 3 is unlocked
- gather Materials for 3x any Grade 3 Mod and 3x any Grade 4 Mod (Miners will likely look for any Mod that needs i.e. Osmium or Platinum, otherwise look for common stuff one can buy like CMM Composites etc., which aren't sold only in certain parts of space)
- spam 3x G3 and 3x G4 mods and voila, Grade 5 access is now unlocked for later use
(crafting 3x Engineer Mods of max. currently access Level completes that entire access Level; 3x G1 Mod at initial Access Level 1 = unlocking Grade 2 Access. 3x G2 Mod at initial Access Level 2 = unlocking Grade 3 Access...)
About 30-33% Grade 3 Access will also get you an Invite for the linked follow-up (Referral) Engineer if the basic requirements for the invite are met (those vary with every Engineer).
Essentially, this is by far the fastest method to gain and extend/progress access with Engineers.
As others already said, a few Upgrades carry rather extreme downgrades and can actually downgrade a Stock Weapon (pending future rebalancing as is planned soon(tm) ).
Most upgrades, however, are very distinct and extremely useful. Once the "bad apples" are sorted out and the "sweet Oranges" are identified (classics like i.e. a nice G5 FSD Range Boost)... go for it.
PS.
In order not to go insane finding out everything needed (as usual, in-game tools are
extremely poor when it comes to providing any useful Information) :
http://inara.cz/galaxy-engineers
With all above in mind, working Engineers becomes
much, much more intuitive, practical, plannable and more enjoyable.