From my POV, karma was really easy to get, and I had heard this from other players that are newer as well. Which seemingly indicates that long-term players may have a disadvantage here because of the decades (possibly) of back-and-forth with different staff of differing values, either because of player bias in being worried about putting one in and being denied, or staff bias, or both.
I highly support being able to access high karma things more quickly. An automatic karma is a great idea. The second karma should come 6 months after that, which means at that point you can play 3 karma roles via spec app. Players that have been around forever and are stuck at 0 or 1 karma should be able to put in a karma request right now. I don't know if it would help, but I'd gladly post my redacted third karma request - maybe having examples in the help file would be useful?
High karma is supposed to go hand-in-hand with thematic difficulty. The thematic learning curve in Arm is very hard because there are not many OOC resources to draw upon. There are old help files, but I can't read back-and-forth debates on the Sun Runners, for instance. And even in the Sun Runner docs, a HUGE amount of their history is lost that is included in other clan docs. So to really understand the full theme of the Sun Runners it takes a lot longer than playing them once, or twice, or even just that clan. That applies to a lot in the game, and 3 karma players should be playing to theme, have characters with personalities that they stick to, and for that reason I think a third karma should take longer to get, a year after the second. A 3 karma player should be teaching others the theme of the game where they play.
I also support karma docking, and being very transparent about why that is, and being able to point directly to reasons. There should be no room for back-and-forth if there is a dock, it should be easily understood by any reasonable player of the game, because there are documented things to point to and post.
For accountability: I suggest adding a personality requirement to karma-holding players, or karma-locked races/guilds (optionally left open for anyone), similar to background. Using bios, it should be possible for to grow and change your personality via life experiences. When a player complaint is put in, those can be referenced to explain why a character acted in such a way, along with references to your background. This is honestly a bare minimum requirement for almost every roleplay-required game I have been on, and I think it would be very beneficial here.
For weight: I think it would require a very obvious, egregious violation for a karma deduction. Misunderstandings happen. If there was a misunderstanding and the player complaint is resolved without action, as much reasoning as possible should be given to the player that put in the complaint. Meaning more, "the player did this because X and X, and given their other options of A and B, they thought this would be more inclusive for roleplay" than "they had good reasons."
For process: I do think that any karma dock should be made public and as transparent as possible within the rules of the game, not as punishment, but in the interest of building a culture of "working together" and encouraging players to grow. They should be able to re-apply for karma as soon as they'd normally be able to, however.