A dev posted that budgets are near infinite but based on what you tell it's the same with you.
When you start a game HOP doesn't have much and in my case they couldn't even build ships. Just grant them access to wares and they start to build 10s of stations. Their state regarding eco or warships does not matter at all in expansion rate.
I bet if you just built good amount of production lines for argons they would build a lot regardless of their current state.
I never saw any faction have more then 1 carriers and 5-10 destroyers the same time. Kept boarding all the L and XL warships at some point and there wasn't more then that even though i had good sat coverage.
HOP didn't even have a carrier during first 200 hours.