Making Lawful Search a spell that can be cast by units feels more against that spirit of spells than converting Lawful Search into an upgrade feels against the spirit of upgrades to me. It’s true there are units that can cast spells, but IIRC they are all tech III and specifically designed to be spellcasters. It’s not completely out of left field, but it feels like a stretch to me.
More practically, doing that would only address one of the 2 goals of my proposed Lawful Search change: the ability to play it before committing to a hero play (edit: and not very effectively, as the $1 or $3 cost to play an Administrator would hamper the ability to afford a hero on turn 2.). Blue also has a consistency problem, where it needs to rely on being able to get information and/or force a card draw on a specific turn in order to remain stable, and making Lawful Search an upgrade is largely intended to facilitate that by allowing it to be floated to a future turn by sitting in play until needed. As it stands now, often when Blue desperately needs to know what Black is holding, Lawful Search is unhelpfully sitting in the deck or discard pile.
Overall, though, good analysis IMO.