If by "maps" you meant mt. myoboku cultivation, then you only missed benefit hall and ninja scrolls I believe. Yes, you get initiative from upgrading battle armor.

Most effective way is using multiples of 1050 cave keys during cave key rebate, that way you will upgrade your runestones and treasure tool at the same time.

Upgrading your refinements is also a very good way of gaining initiative. Headband charm also gives a decent amount at lvl 9.

5 natures chakra isn't really worth it past stage 2 unless you maxed out your runestones/refines/charm on position 1.

Myoboku cultivation also gives a nice amount for a low price at early stages. Summon cultivation doesn't give much, but it'll add up eventually.

Also try to collect all clothings which give initiative. They may not be the best option for your move 1 ini, but they are definitely the best option for acquiring total initiative.