I think the problem may be with your strategy, not with the game. Here are a few tips:
Specialize worlds: Because everything runs off of % modifiers now, it is much more efficient to have each of your planet produce research, wealth, or manufacturing, rather than having them do a little of everything. For research and wealth worlds, I usually set the circle to 50/50 manufacturing and research or production until I've built my buildings, then switch to 100%. I do the same for the balance between social and military spending on manufacturing worlds. I generally do not set wealth or research worlds as sponsors to shipyards. There may be some justification for doing wealth/research and/or wealth/production worlds because of the 50% bonus to production from 100% approval, but I think straight specialization is still better.
Don't worry about approval: Your research and manufacturing worlds will still produce a ton with 0% approval, and your wealth worlds will always have 100% approval. Approval buildings currently don't do enough to be worth building.
Mind your adjacency bonuses: These will often be worth more than your buildings' core bonus. Also be aware of any bonus tiles and how their bonuses compare to any adjacency bonuses they might cost you.
Grow your population: Population produces the raw production that turns into wealth, research, and manufacturing. It is important to grow your population as you build other improvements, Population growth is essentially multiplicative while production bonuses are additive. If you have a planet totally devoted to research with 10 population and +100% research, a building that grants 20% to research will increase your research from 20 to 22, while a farm that increases your population by 2 will increase your research from 20 to 24.
Keep Shipyards close to their sponsors: Shipyards have no penalty when within 6 tiles of their sponsor(s). More then that and you start loosing manufacturing (I've heard 10% per tile, but haven't checked it). Those red numbers by your list of potential sponsors are how much they will contribute after penalties.