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The name <b>Antichess</b> is used in many places as alternate name for <a href='../diffobjective.dir/giveaway.html'>Giveaway Chess</a>, otherwise <a href='../diffobjective.dir/anti-king-chess.html'>Anti-King Chess</a> would have been likely called that.
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The game you describe has some simularity to my game of <u>Sacred King</u> (found on the hard-to-locate Modest Proposal - Various Authors page <a href='../other.dir/modest-various.html'>here</a>), but the creation of pieces when you move might avoid the tendency of Sacred King to be endless.
Your first rule is the same as the first rule in Parton's game Contramatic Chess.
So how do you get the pawns out of the way of the pieces in the back row?
Contramatic Chess can be found about two-thirds the way down <a href='../parton/Curiouser&Curiouser.txt'>this</a> page.
First tests: Rule 2 makes the game endless in many cases: Pawns are not good pieces for this game. On the other hand, Contramatic exists, I have made a few tests with it, and I dislike the game play, but this is only my modest subjective opinion. Anti-Chess or something else around this idea: Rejected project, at least by my part, it was only an exploratory idea.
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