I thought it was relatively clear in the translation here and the fan-translation that this is one of those Client Orders that can be accepted and turned in on a weekly basis in the exact same way Klotho's/Chroto's Client Orders are. I recall telling you that they were not exploitable because it was your weekly source of Meseta that has been made significantly easier ever since ARKS Missions have been introduced on the Japanese side (which was shortly before Episode 6's introduction).
With more than one character you can summarize the math to being about 2.6 million Meseta per character on completing all of the Weekly Missions and the Yerkes Client Orders compared to the older 2.2 million Meseta per character (completing Klotho's Client Orders and Yerkes' Client Orders). On top of this, Yerkes' Client Orders are trivial because you have more than enough time to gather the resources and stockpile them. Before the release of the Hero I gathered all sorts of resources to create a multitude of Critical Strike (R) rings and other high-value rings to fully upgrade them and sell them on the Player Shops because there are still a large number of players who don't upgrade their rings or invest in anything further than the game's freebie rings (Atomizer Lovers (L) and Boosted Enemy Slayer (R)). If that's still too much for you, you can even create the Forest Tomato Salad and put that up for sale for a decent price (50,000 Meseta per salad) for the new players who for some reason don't have Forest Tomatoes which are easy to get but are willing to throw money to get one instead.
And lastly I suggest learning to budget even if you aren't planning to spend all that much in the first place. What is it that you need your Meseta for that you're upset with how little you have? Is it to gear up and buy your way through equipment? Is it for upgrading/affixing (which is currently free at the moment so I highly suggest you taking advantage of this if you have not)? Is it for fashioning and keeping up with the trends? There are a lot of ways to make Meseta relatively easily and at the same time make progress on all of these fronts. For instance, I would heavily recommend running the solo Profound Darkness trigger (Rising Badges 3) so you can stockpile on resources and Excubes. The excess twelve-star weapons become desynthesis fodder which can be turned into the related gold and sapphire resources (highly valuable for our current fifteen star weapons) and the extra ten-star and eleven-star weapons (which will later apply to twelve-star weapons in the future) can also be turned into Excubes. If you get a full stack of 999 Excubes and turn them all into Grinders (33 Excubes = 990 Grinders) and sell this stack to any in-game vendor you can anticipate 396,000 Meseta per stack. A full stack of 999 Excubes then translates to about 11,988,000 Meseta.
If you have a Player Shop Pass you can further jump into this by running onto the affixing fodder hype by collecting and stockpiling items that have high numbers of abilities loaded onto them such as units with six, seven, or eight abilities. The same goes for weapons as these can be filled with junk affixes to help with upslotting as long as it has eight slots. Otherwise you can jump onto the bandwagon and hunt for things that are in high-demand such as the Rappy costumes from the Thanksgiving event (or encountering any Turkey Rappy). If you would believe it I managed to sell an Orange Rappy costume from the Halloween event when the prices for those were astronomically high (100,000,000 Meseta) before they immediately tanked due to the Thanksgiving event giving those out more easily.
And for me to state this at the end, you are wholly incorrect in that the cooldown a character has is tied to the whole account. There is a reason why "on average" with three Level 50 characters you should end up with 6,000,000 Meseta per week. You can even see this clearly when you look at your ARKS Missions and realize that each character can claim the rewards there separately. The only things that cannot be claimed multiple times like this are one-time rewards that are account-bound (like Title Rewards and the specific items obtained from ARKS Missions, and the Tier Missions Rewards that increases your rank). Everything else is character-bound and as a result is repeatable provided the character has not yet done them already to go onto cooldown with.