Roger le dodge.
Well i built a thing that may suit your needs.
I present to you, the Palletised Payload Lift System.
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Comes in 2 sections. The Pallet carrier and the fuel/lift Truck.
Pallet Carrier
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Completely modular and complex looking but it solves the problems of doors and landing leg lifts. Happily capable of wandering around with 90+ton payloads, dimensions of the pallet mean you can make it as wide as the biggest fairing and as tall as you like without modifications to the base system. Just plonk your payload on top and press go.
Fuel/Lift Truck
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The brute of the pair. Will move under its own steam but at nearly 700t it doesn't like it much. However, when connected to the Pallet Carrier it'll make a good 5m/s across the pad.
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Contains 549 tons of fuel and lots of RTGs to provide power/fuel re-supply whilst you're loading the pallet on board. I didn't know how much you needed but from the size and make up of the black fuel tower you were using I guessed 427.5 tons. Gives you some extras incase you decide to go bigger.
Speaking of going bigger, I left some play in the upper lift system and didn't fit any connectors to your rocket. So you can fit them yourself at whatever height you like and it will go another 8 or so squares up as well without adding more lifts. Just move the last stopper and extend the roof accordingly
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Does it work? Yes. Yes it does.