Another way to make it functional is to make death in pvp actually meaningful. At the moment, there's very little incentive to attempt to kill an attacking player, because doing so only costs them a small amount of credits and a few minutes to jump back to the fight. You buy yourself a short reprieve at best. This discourages pvp in general, because the reward for victory is so small, relative to the difficulty of achieving it. Why fight for 15 minutes for a 5 minute break?
Other games, such as Runescape, have created very enjoyable pvp areas by making you lose your gear when you die; I don't think this would be a good solution for Elite, (because it doesn't have the same pvp restrictions as Runescape, where almost all pvp is limited to very specific zones outside of duels), but we might use that as a guideline for the sort of thing that makes pvp more enjoyable.
For example, maybe have players with more than 1 notoriety have their ship impounded at a prison ship that refuses docking access or ship transfers for anyone with notoriety. The player would need to wait for their notoriety to fade before being allowed to regain their ship again. Players could have multiple ships to attack in, of course, but doing so would continue to increase their notoriety, and eventually, they'd need to wait for it to go away before being able to reclaim their confiscated ships. (the 'more than 1 notoriety' bit is to prevent abuse of suiciding into players to give them notoriety).
They essentially 'lose' their gear when they lose the fight, driving up the risk(and, by proxy, enjoyment) of engaging in criminal pvp. And while this might seem to be only a punishment for nonconsensual pvp, I think that on the contrary, it would actually get people a lot more good fights. Right now, people have no reason to do anything but run; with some stakes, people will be much more likely to actually give it a shot.