ya, running rca's with the power wire will cause engine. i have installed a lot of line out converters and seen no problems. maybe the shop you went to has cheap line out converters. i would run the power wires down the driver side(i have not idea where your battery is but i am guessing) and run your rca's down the passenger side. if it is easier for your to run the power wire down the passenger side then run the rca's down the driver side but DO NOT run them in the dash(up by the pedals and suff). If you tie it up to the wrong harness it may be an ignition harness which will cause you to have engine noise. Just run it under the driver side carpet(the foot area only) unitil you get it to the side, then go straight down.
also, if you do buy an amp with high level inputs keep in mind that it also has a line out converter but its just built in so i do not see why the other installer would be right. i did a 4 channel amp(for the 4 speakers) in a MDX w/navi system the other day and we used a 2 line out converters for the amp and there was no noise at all. in my own opinion you might be better off using line out converters with both amps. all you would need is two, one that taps into the front speakers and one that taps into the back. you can either use rca splitters on the line out converter for the rear and use that one box for the rear channel and the sub amp. also i know METRA makes a kit for the US 04 accord with includes the climate controls and cost $200. if its the same dash you may be able to use it.