Weekly cap is 66k moon scrolls (at least at lvl 99 where I'm at). That's 330 keys per week = at least 1320 keys per month. F2P should be able to do 2.1k cave key rebate every 3 months, if you count free cave keys from tree and events. Of course that means neglecting other redeemables, but cave keys are by far the best choice there, especially with runestones not maxed. Bells are also a good choice, but you also need to invest sun scrolls in elemental bond scrolls, which will mean neglecting adv. refines...

"After level 9 runes in move 1 bells up to level 9 assist links, myoboku gifts up to page 13/14 and even advanced threads up to rank 7 BA are way way better investments goodpower-wise and initiative-wise"

Power wise - sure, initiative/p1 strenght wise - I have doubts, maybe if your p1 charm has very low lvl. And BA is just IMO not worth it. Lvl 6->7 BA would take about 240000-320000 moon scrolls if i were to redeem it from shop (57/100 currently, I'm not expecting level up before 90/100). With that I could redeem 1200-1600 cave keys which seems way better even if you have high level runestones. With level 7 charm upgrading your single runestone from 10 to 11 will give you 276 of secondary stat (BA 6->7 gives 200, although for every position), and that's not counting Treasure Tool.

I agree with leveling assist links, not sure if you should do it at level 9 runestones or later, but they give a nice boost. Not sure about myobokus, will need to take closer look at it, but non freezers can get at least 3 myobokus per day for free.