Those generalist qualities can be very valuable at a large company, if you can handle the politics. Main thing is you probably will have a hard time going in through the front door as there are generally too many gatekeepers filling checkboxes. You need to go through the hiring manager or leadership recruiting directly to be able to tell your story to people who will get it.
This is great advice. Generalists have to engender a high degree of trust before they are considered reliable for some set of tasks, and if no one at the company knows you then it will be hard for you to demonstrate your skill set effectively. Telling the story of how you got those skills to management (and having good references to back it up) is pretty much the only way to gain that trust without already being in their network.
I can barely pass technical bars because the last few times I interviewed I didn't understand the game well enough, but the second I'm in anywhere I start to get massive amounts of work done and make projects succeed on less code simply because my non-dev experience.
All big companies need and hopefully develop some people who are like this - its certainly part of the role I and few others had as the GOTO fixers.
This could vary from finding /building a pc for a new start when some one had forgotten to order a pc for them, fixing the BACS tape, doing initial deployments of systems including taking enough kit with us to build a network in case that had been forgotten.
The most interesting one was cracking nt4 to break into a client system - I got a break just on a power mac and didn't need to actually use all our sun workstations after ours to run a distributed attack (BT security / Squirrels) might have not been to happy (yes I did get authorisation)
