While I haven't done much tritium mining yet, I did get myself back to the bubble from Colonia mining over half the required tritium. At least in a tritium hotspot, tritium "wells" (sub-surface deposits) are very common and I was able to get 200t in about an hour easily enough (nicely over 1000ly range in a lightly loaded carrier).
However, I have yet to find a single tritium core, and I very much doubt I will. Surface (laser), nodule (abrasion), and sub-surface tritium makes sense, but not core because anything in a core would have decayed long ago, while the surface and shallow stuff would be generated by local radiation interacting with the materials in the ice.