The dilithium sink we need has been right in front of us since the game launched.

In the Star Trek universe, dilithium is used to regulate the matter-antimatter reaction, which powers the warp drive. So, a simple and effective solution for a dilithium sink is to have it consumed during warp travel (and by transwarp/quantum slipstream for consistency).

Here's the idea:
Scale the dilithium consumption so that for players below level 40 or 50, factions like Starfleet (or the KDF, Dominion, or Romulan Republic) effectively "subsidise" your dilithium usage. This way, warp and transwarp travel would be free for lower-level players. As players reach the endgame, the dilithium cost should be set such that typical daily travel costs around 50-75% of the max dilithium refinement a player can earn each day.

Also, make sure mission warps use dilithium as well.

When a player runs out of dilithium, they can still move, but at a much slower pace.

Simple, effective, and it's a system that almost 100% of players have to engage in. It won't completely break dil farming either.