^This.Try the Squire Debut Series P Bass available only on Amazon. $130. You can modify the nut the way you wish and go BEAD with little remorse.
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Go with a squier P from the debut or sonic series and mod away. If you need to drill out the string hole in the bridge for the thicker B string, no biggie. Tusq makes a precut nut, basically a drop in replacement. Also the thin j style neck and lighter weight are great economically speaking. I’ve never played a BEAD bass with a P pickup, but I don’t think I’d be disappointed.