So basically if you want shake and bake shipyard, you'll want to go for a constellation of components rather than trying to build a single huge factory. Economies of scale exist, but with the number of components that a ship requires, you're better off spreading that out anyway.
Here's my idea. Everything is built as jump capable modules.
Yard
Mass: 60,000 tons
Technology Base: Inner Sphere (Advanced)
Introduced: 3060
Mass: 60,000
Battle Value: 3,744
Tech Rating/Availability: D/X-X-D-D
Cost: 10,096,620,000 C-bills
Fuel: 250 tons (2,500)
Safe Thrust: 0
Maximum Thrust: 0
Sail Integrity: N/A
Heat Sinks: 82
Structural Integrity: 1
Armor
Nose: 46
Fore Sides: 38/38
Aft Sides: 33/33
Aft: 20
Cargo
Bay 1: Standard Repair Facility (Unpressurized) (400,000)1 Door
Bay 2: Mech (30) 3 Doors
Bay 3: Small Craft (20) 4 Doors
Bay 4: Cargo (36007.0 tons) 1 Door
Ammunition:
180 rounds of AC/2 ammunition (4 tons)
Dropship Capacity: 0
Grav Decks: 1 (100 m)
Escape Pods: 0
Life Boats: 0
Crew: 11 officers, 49 enlisted/non-rated, 1 gunner, 160 bay personnel, 400 passengers, 30 marines
Notes: Equipped with
1 Field Kitchen
260 tons of standard aerospace armor.
Weapons: Capital Attack Values (Standard)
Arc (Heat) Heat SRV MRV LRV ERV Class
FRS/FLS (1 Heat)
1 AC/2 1 0(2) 0(2) 0(2) 0(2) AC
AC/2 Ammo (45 shots)
ARS/ALS (1 Heat)
1 AC/2 1 0(2) 0(2) 0(2) 0(2) AC
AC/2 Ammo (45 shots)
Note that this is not a "shipyard" this is just a yard. It's a scaffolding within which to assemble the varied components into a ship. There's also berths for industrial mechs and smallcraft for shunting stuff around, and life support for union mandated lunch/downtime for the on duty shift. For zero g heavy labor in the harsh vacuum of space, you want to make sure that your workers are always in tip top shape. That means at the point when your workers start to waver, you pull them off the line to get them fed, napped, and caffeinated before resuming work.
Like the Utopia Planitia yards in Star Trek. Or regular shipyards in real life. The ship is basically being assembled in a big hole in the ground surrounded by cranes and shit. All of the big finicky stuff, assembling modules, is being done over there.
Housing
Mass: 60,000 tons
Technology Base: Inner Sphere (Advanced)
Introduced: 3060
Mass: 60,000
Battle Value: 3,744
Tech Rating/Availability: D/X-X-D-D
Cost: 117,900,000 C-bills
Fuel: 250 tons (2,500)
Safe Thrust: 0
Maximum Thrust: 0
Sail Integrity: N/A
Heat Sinks: 82
Structural Integrity: 1
Armor
Nose: 46
Fore Sides: 38/38
Aft Sides: 33/33
Aft: 20
Cargo
Bay 1: Small Craft (20) 4 Doors
Bay 2: Cargo (41531.0 tons) 1 Door
Ammunition:
180 rounds of AC/2 ammunition (4 tons)
Dropship Capacity: 2
Grav Decks: 1 (200 m)
Escape Pods: 0
Life Boats: 200
Crew: 10 officers, 47 enlisted/non-rated, 1 gunner, 100 bay personnel, 1200 passengers, 30 marines
Notes: Mounts 260 tons of standard aerospace armor.
Weapons: Capital Attack Values (Standard)
Arc (Heat) Heat SRV MRV LRV ERV Class
FRS/FLS (1 Heat)
1 AC/2 1 0(2) 0(2) 0(2) 0(2) AC
AC/2 Ammo (45 shots)
ARS/ALS (1 Heat)
1 AC/2 1 0(2) 0(2) 0(2) 0(2) AC
AC/2 Ammo (45 shots)
You generally want to put your workers in "housing" if they're not going to be commuting from the surface every day. You could probably accomplish this with burrows, but not everybody knows how to do that so you want a dedicated station as the core and you can anchor burrows from there.
Vehicle Assembly
Mass: 60,000 tons
Technology Base: Inner Sphere (Advanced)
Introduced: 3060
Mass: 60,000
Battle Value: 3,744
Tech Rating/Availability: D/X-X-D-D
Cost: 100,615,000 C-bills
Fuel: 250 tons (2,500)
Safe Thrust: 0
Maximum Thrust: 0
Sail Integrity: N/A
Heat Sinks: 82
Structural Integrity: 1
Armor
Nose: 46
Fore Sides: 38/38
Aft Sides: 33/33
Aft: 20
Cargo
Bay 1: Small Craft (20) 4 Doors
Bay 2: Cargo (15000.0 tons) 1 Door
Bay 3: Cargo (6000.0 tons) 1 Door
Bay 4: Cargo (6000.0 tons) 1 Door
Bay 5: Cargo (6000.0 tons) 0 Doors
Bay 6: Cargo (1000.0 tons) 0 Doors
Bay 7: Cargo (1000.0 tons) 0 Doors
Bay 8: Cargo (1000.0 tons) 0 Doors
Bay 9: Cargo (1000.0 tons) 0 Doors
Bay 10: Cargo (1000.0 tons) 0 Doors
Bay 11: Cargo (8407.0 tons) 1 Door
Ammunition:
180 rounds of AC/2 ammunition (4 tons)
Dropship Capacity: 2
Grav Decks: 1 (100 m)
Escape Pods: 0
Life Boats: 100
Crew: 10 officers, 50 enlisted/non-rated, 1 gunner, 100 bay personnel, 600 passengers, 30 marines
Notes: Equipped with
1 Field Kitchen
260 tons of standard aerospace armor.
Weapons: Capital Attack Values (Standard)
Arc (Heat) Heat SRV MRV LRV ERV Class
FRS/FLS (1 Heat)
1 AC/2 1 0(2) 0(2) 0(2) 0(2) AC
AC/2 Ammo (45 shots)
ARS/ALS (1 Heat)
1 AC/2 1 0(2) 0(2) 0(2) 0(2) AC
AC/2 Ammo (45 shots)
Going with the provided specs for the small and medium factory, this module has space for 5 small factory modules, 3 medium factory modules, and one large module. And then a pressurized bay for assembling the ship module that would be pushed around by tugs and stuff once it's completed.
And of course, there's basically no possible way to dropship modularize a KF core forge. The job is just too damn big. Not saying you couldn't ship it over as modules, but I'm assuming that what is expected is components that you can ship like dropships.
So basically once you've got the core forge set up, you'll want to put a yard, a housing, and a vehicle assembly on an Invader class dropship and ship those over to the job site where the individual stations can then undock, boost on their stationkeeping drives into position, and begin low rate production immediately. From there, you can expand each site by shipping over additional modules, another yard if you need work on another ship at the same time, more housing for more workers, more vehicle assembly to speed up work with parallel production. Etc.
It's not as "efficient" as a single large station that can do everything, but it does get set up quick, and it means that the workers over at Galax/New Avalon can just keep cranking the same design over and over again which isn't as exciting as bespoke builds or warships, but it keeps your C and D teams productive.
Also, with a constellation approach it disaster proofs your shipyards quite nicely. For example, if for whatever reason ROM decides to nuke your shipyards, you lose the module station, but by the time the blast has propagated through space it can't do much damage to the other modules. It hits the production rate, or even loses the current project if they hit a yard, but at least production continues rather than grinding completely to a halt.