Yamato's distribution will be a huge problem... the galaxy is just too big, and ships take ages to travel across it. I dunno if this is doable but I think that a solution to this issue might be to create a parallel dimension where only legendary planets exist. Let me elaborate more:

This is how our alpha to delta ring looks like, deploying Yamatos here would be insane since 99.99% of the players would have no chance to actually fighting them.

But if we can have some kind of parallel dimension, where only legendary planets exist, a parallel dimension which would be the spawn areas for Yamatos, and are accessed by other ships through wormholes evenly distributed alongside the whole galaxy... it would give a chance for every player to fight a Yamato even if his headquarters are located on the corner of the galaxy.

You can fill that hypothetical parallel dimension with even more rewards for legendary planet owners, and for other players as well... like stardust generated by supernovas explosion (an event where stardust can be collected if you control certain are after such a supernova explosion, after all the dust in the universe is formed after supernovas explosion lol).

It can also give more incentives for players to buy in-game items such as special ships for collecting that stardust, etc. Ingame incentives to pour money into the game is what will make the economy of @nextcolony to flourish.

Anyhow, let's wait and see how this first test turns out.
Best regards.