After 8 solid hours of trying again and again in sandbox, I finally put a space station in orbit. Screenshots below!
The rocket is a five stage design (though the game counts it as ten stages). Eight Rockomax BACC SRBs assist with initial liftoff, supporting three Rockomax "Mainsail" LFEs each with their own Jumbo-64 tank. The main engines cannot be pushed past 2/3 power or the entire rocket will literally
tear itself in half with the overwhelming thrust capacity.
Once the SRBs are expended, they are jettisoned and the main engines are pushed to their limits. Within seconds, we've cleared the atmosphere.
Once the massive tanks are empty, they too are jettisoned. The second stage is lit, and burns for the next several minutes to bring the payload up to about 100k altitude. A 45° angle is introduced to set up the orbit path. This part is very tricky, as even this single engine can tear itself in half if you turn too quickly. On the other hand, constant course corrections are required even after you find your target.
Once the second stage is empty, the next part happens almost instantaneously as soon as it is triggered. I was (after 3 tries), unable to get a good screenshot of the separation. Four smaller SRBs light up and power the whole ship halfway through its orbit. Why only halfway? Because no single stage I could come up with would push something this heavy all the way into orbit. This part is extremely difficult, mostly because you can barely guide these things, and they have so much power. Not ideal for delicate jobs at all... which is why we're not done yet.
Once the boosters are dead, they're jettisoned as usual and a smaller engine finishes the burn for me with more careful aim. Once I've gotten to this point, I'm already in a solid orbit. The rest of the fuel goes towards matching the 100k orbital on my periapsis.
Finally, I'm done with the hard stuff. One final job (the fun stuff) is left to do! Jettisoning the engines and turning the rocket into a proper space station, I align myself as desired and begin to deploy my solar panels and instruments...
The final product. Space Station Kat! ... or a GDI Ion Cannon, if you prefer.
I am very proud of my work, honestly.