I realize this might be a bit complex to get the mechanics right, but....
Allow construction factories to add to the capacity of SY, create new slipways, and/or build SY with initial sizes larger then 1kton/1slipway.
At present I'm running a 10billion pop conventional campaign (seeing if bigger industry can overcome tech disadvantage vs. NPR), so my industrial base is 10x what it normally is.
The good news is that almost everything is scaling well (it's amazing how fast research gets done with 100+ labs

, although I do see some data-management issues looming on the screens for ground units, officers, SY management etc - basically anything where you need to control individuals becomes 10x harder when you have 10x of them.
The one thing that isn't scaling well is the lag time in SY to build many or large ships. Basically, once you've built a SY, you have no way to speed up the growth of the SY - once the initial yard is built, it takes the same time to expand the capacity of a SY to make capable of constructing a super-carrier whether you've got 100 construction factories or 10,000. One of the things that I think would be fun in this 10x game would be to a few 100kton warships rather than 10x 10kton warships, but I'll need to wait decades for my new SY to grow big enough to manage a 100kton ship.
Two thoughts of how to do this:
A) Allow construction factories to be assigned to SY for the purposes of their expansion tasks. These construction factories would be taken out of the general industrial pool, i.e. they would get "first dibs" on the factories before the various percentages of the other stuff was factored in.
B) Add "expand capacity for SY X" or "build new slipway for SY X" to the possible industrial tasks. The management problem here is coordinating between the industrial tasks and the growth task of the SY itself. An extreme version of this would be to remove the ability of SY to grow themselves from the SY - just turn it into another industrial task (I'm not sure I like that idea due to micromanagement concerns on the industrial tasks screen - I think I prefer #A above).
Note that, once the SY is built, I can speed up construction of large ships by creating prefab components - I was originally skeptical of this idea when it was introduced, but now that I'm using it I love it - it's simply getting a SY big enough in place that's the problem.
A few minor suggestions for managing 10x games that I thought of while typing:
1) Allow SY to be set into a "continuous construction" task, where it automatically starts a new ship of the same class whenever the previous ship finishes. This would cut down on micromanagement of series production.
2) When building prefab components, add a command that allows you to build the prefab components for an entire ship class as a single task. At present, I'm spending a lot of time adding tasks for 5 ion engines, 1 active sensor, 1 thermal sensor, 1 EM sensor, etc. and coordinating their percentages so they finish at the same time, all to prefab the components of a single ship.
2') It just occured to me that suggestion A above could also be used to make prefabbing easier - allow industrial capacity to be dedicated to SY construction tasks too. I'm not sure you're going to like this one though (which is ok), since you want to make it hard to switch SY abilities around. On the other hand, the retooling cost/time is still there, which adds switching time.
3) I'm not having a lot of luck with the current numerical rating system for prioritizing officer assignments to classes in auto-assign. How about a new dialog/tab on the Commanders window that allowed you to pick a level of commander - it would then present all of the classes which that level can command as an ordered list with up or down arrows. The class ordering could then be adjusted by hitting the arrows. Level of commander would still be controlled by the DAC tab of the F5 screen - it's just the priority of the classes for getting commanders that seems hard/cumbersome.
4) Some way to group ground units into "commands" that can be minimized, without requiring the building of HQ. Actually, I think someone else (Waresky maybe?) has suggested something similar for TF/TG. In the TF/TG version, the F12 screen would have an additional pulldown selector for "TF being viewed" (which would include "all" as an option). If the TF was set to e.g. "Exploration Command", then only TG in Exploration command would show up TG selector. The "command" idea for ground units is similar - a command wouldn't have any game mechanics significance, it would just be a tag that could be filtered against. As a concrete example, if I end up with 100 Marine companies, each on a ship, my "all ground units" screen is going to be a nightmare because I can't put them into an HQ.
John