Regardless of the class in question
Imo, regardless of class being discussed 99 percent of players can't even to think about 5x3+1. it's similar to winning a lottery regardless of the amount of lost ark gold. It's not going to ever happen to most players until we discover ancient things.
5x3+2 would be useless to discuss because only a few people will be fortunate to be able to obtain it.
Therefore, arguing about what to consider as the primary component in the best build would be pointless.
While the red gunlancer 5x3 class is less expensive than other classes, it's easily 50k+ for accessories along with 20k+ for the +12 master brawlers if you're opting for the cheapest alternative. The books cannot be used to create any other class other than destroyer. Imo If you're not the principal character and you'ren't whining, 4x3+1 is enough. It's true that CR isn't going to be available every single time you use mechs and such, however it is a good time-span and most importantly, at item level it lets you soak one hit every now and then to trigger your burst unlike 5x3 which means shields are destroyed in one go and you're left without shields when charging the surge cannon.
I bought myself an 4x3+1 for 8k gold total, with pheons too. Grudge, supercharge brawler, Lone Knight as well as combat readiness lvl1. It is extremely effective, and will still be able to take some attacks here and there, and as an alt that I can upgrade my gems from lvl7 to tripods to +4 without investing 50k+ to purchase a the cursed doll, instead of lvl1 combat readiness. So , if you don't own the +12 grudge or supercharged books already, I'd suggest against using gold lost ark. Master brawler is not worth the cost for roster.
For adrenaline, with fire bullets it's very simple to maintain. However, I'm not sure there's any benefit to run it. Other engravings are more effective like you said. It is possible to get one swiftness ring and have 1400 crit that's more than enough even with lostwind. You can get 85% with 1400 crit, the lone knight, and an the entropy set. There is also a swiftness ring. It's 700 total swiftness, 112% ms or percent with desire. Plenty.
People speak about attackspeed and movespeed for speed, but 100 swiftness equals 2 cooldown reduction of 2%, which means the ring you choose gives you percent. It's like when you upgrade all the cooldown gems you have by two levels.