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Installation drive.
"And most applications still want to install to the C drive, especially everything from Microsoft."

So override the default and install to an external drive. Yes, you're going to have to lug that around too, but I suspect if you're installing enough apps to fill the drive, a tablet may not be the best device for you.

Just one ignorant opinion based on a complete lack of practical experience, you understand.
Updated - 31st Jan