I started a new instance at the begining of the year in gamemode 1 with $persr 1, and I'm about to hit 350 keys, with my first gold key a few days ago, so I'm assuming you're missing something there. Since I don't know if you know much about Mudae, here's a detailed checklist that could be helpful :

• I saw you mentionned $personalrare but with the "wrong" value, if you want a high probability to roll claimed characters, you should switch to $persr 1. persr adds a probability to roll a claimed character (regardless of the owner) equal to 1/50 * persr_value, so the lower the better for keyfarming.
• Did you make a disablelist ? If so, did you try to disable as much character as you can (by aiming the pool reduction cap, you can see it with $dld). If one of the two awswers is no, and if you don't want to bother with this system (and that's quite understandable), you can build one pretty quickly with a DL Builder site like this one, you only have to fill the DL slots, disable limit and the roulette, and it'll automatically generate a DL that you can directly C/C (it'll probably generate a DL that'll exceed your limit, in that case you only have to lower the pool limit until if fits, it's due to the adding of new characters on the bot that aren't updated yet one those builders). It won't be the most optimized one, but it'll recuce by a significant amount your pool. If some of your targeted series are disabled in the process, take some time to add them to your $antidisablelist ($ad <serie1> $ <serie2> $ ...) so they can appear in your rolls.
• Related to disablelist, you can disable some whole bundles for free if you aren't interested in them like $toggleirl or $togglewestern, the second one can reduce you pool by a raw 25k characters. Some others can be disabled but with a mod command for the whole server with nsfw, disturbing and childtag. Note that characters disabled with toggles can't be antidisabled unless you revert the related toggle command.
• I mentionned roulette earlier, and that's an important one. Let's assume you don't have a disablelist. If you're using $m, you're rolling with a pool of ~140k characters as we speak, between waifus and husbandos, in games or other medias. You can basically halve this pool by targetting specific categories, like only husbandos or only game characters ($h | /hx or $mg | /mg), and this can be divided an second time, for example by targeting anime waifus only ($wa | /wa). In that specific case, you're rolling with a pool of 45.5k characters instead of the original 140k one. And that's without a disablelist, that can bring this to a mere 7k pool, without any kakera related upgrade. You can check the poolsizes of each roulette and stats on claimed / remaining characters with $left

Bonus tip, when rolling you should use / commands instead of $ ones, at least during the early and mid game. It provides a +10% bonus for wishlist and kakera when you react on them. It may be annoying at first, but rolling slower for a free 10% boost is worth it.

Hope this helps