What are the best steps to shortcut in the reactor removal checklist? 
Okay, so your main obstacles to reactor removal are:
* The coolant pipe
* The fuel pipe
* The floor
* The reactor housing
Now, if you want to speedrun things, you can start off by defusing the coolant line. You can do that either by shutting down the ECU (remove front panel, remove small fuel canisters, if fog dissipates, ECU is off), or by just vaporizing the connector between the ECU and the pipe.
If you have a key, you can shut off the fuel line; if you don't, you need to purge the fuel from the thrusters (this may cause explosions, so be quick about it: As soon as all 3 lines are purged, all fires should stop).
Then you cut the floor in front of the reactor with the splitsaw to have a clear shot for pulling the reactor out. Tether it to the barge, and you're done-- unless the barge refuses to register the reactor being delivered, in which case you need to pull off 3 panels and then pull the reactor out of the housing.
(Personally, I'm fine with taking 3 or 4 shifts to get a gecko fully dismantled; The reactor alone pays for all of it, and as you move up the ranks, your running costs decrease drastically once you are able to purchase your equipment)
