I want the same things you do and I use the following strategy:
Let's say, I designed some 36 ships (all saved as templates) and I created different versions from them with functional parts during the game.
I want to start a new game with only designs without functional parts and also only a couple of ships, so one colony ship design, one constructor design etc.
To achieve this I manage my designs outside the game. I copy sets of designs from the templates folder into seperate folders elsewhere named TerranFleet1 or TerranFleet2 for expample. Then I delete all designs and ships in the ships and template dirs. So there's nothing left. Then I decide which 'fleet' I want to use this game and copy them from the appropriate fleet dir in the templates dir.
This way you have a 'clean' dir without any previous designs with weapons etc. popping up. When you research through the tree your larger hull designs will pop up accordingly.
Managing ships outside of the game really indicates that the ship designer lacks some functionality in managing large numbers of ships with and without functional parts and grouping of ships.
One more thing: being able to design your own ships in this game is a GREAT feature and I spent many hours already creating my own fleets.