Here's an ASRock board with 10 Power Phases: http://www.newegg.com/Product/Product.aspx?Item=N82E16813157634&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-PCPartPicker,%20LLC-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=
You'd need the MIR to get it in budget.
Also... out of curiosity, why are power phases so important to you? Are you seeking extreme OCing or something? Otherwise, it's not really a big deal for Intel 1151 processors.