For a basic upkeep cost you could probably give every ship a buff that makes it drain the resources of the owner (stuff like Drain Planet or the Pirates' Plunder ability can drain/steal resources, so it should be possible)

You will run into problems with Scouts, as they already have 5 active abilities, leaving no space for the passive buff-placing one (and no existing passive means you can't add the buff to that ability either) - then again, unless you want to make Scouts viable combat units, I think they shouldn't cost upkeep anyway (seeing as they're self-sufficient vessels supposed to operate deep in enemy territory without any outside support, and gameplay-wise noone will spam them to avoid upkeep since they still cost resources and supply)

This will not stop people from building 2k supply worth of ships, provided they have the resources at hand, but it will drain their resources afterwards and prevent them from building anything else.