Is it OK to run a serpentine belt on a slightly different path if the normal one won't sit right?

I would not leave that routing in place. On my old Taurus I talked myself into a similar workaround after a belt swap, and it turned out the new belt was one rib wider than the stock one, which is why it kept walking off the alternator pulley. Fixed belt, factory route, problem gone. Point is, when the factory routing fights you that hard with all new parts, the routing is almost never the thing that's wrong. The back of a serpentine belt riding a ribbed pulley is a real problem long term. The ribs are meant to mesh with the grooves, and running the flat side against them chews the backing and can oval out the idler bearing since it's spinning against a surface it wasn't designed for. Same issue the other way around, ribs on a smooth idler. Then there's the wrap angle problem someone mentioned above, since your improvised path probably leaves the alternator pulley with way less belt contact than the factory layout gives it, and low contact means slip under load even if it seems fine on a short drive. It'll show up on a rainy night with the headlights and AC running.

Before you cut another belt, go back through the basics with fresh eyes. Check the belt part number against your VIN, not just the engine size, because Ford used a couple of different setups on that 2.0 depending on whether the car has the optional tensioner setup. Pull the tensioner and make sure it moves freely and returns with full spring pressure, no binding. Some aftermarket tensioners ship with a locking pin that has to come out, so double check that if you installed a new one. And verify the old belt versus the new one rib for rib and lengthwise, laid side by side on the ground. Belt walking off one pulley rib by rib is almost always a misaligned component or wrong belt, not a routing puzzle. If the new tensioner pulley is even slightly out of square it'll walk the belt exactly like you describe. Put a straightedge across the pulleys and see if anything sits proud.

Agree with the Taurus poster, the wrong belt thing bit me too. Bought one for my Escape by engine size alone and it walked off the water pump pulley constantly untill I checked the door sticker and it needed the version for cars with the heavier duty charging setup. Also, on mine the idler bearing had started to seize, which tilted the pulley just enought to shove the belt sideways. Spun it by hand and it had a gritty grind to it, so give each pulley a spin and listen while you're in there.

One thing I'd check that hasn't come up yet is pulley groove wear. On my old Ranger the water pump pulley grooves had gone shiny and rounded over after a couple hundred thousand miles, and a fresh belt would climb out of them exactly like you're describing, since the ribs had nothing crisp to bite into. Drag a fingernail across the grooves on every pulley, alternator expecially, and feel for a glazed smooth ridge instead of sharp edges. A cheap replacement idler that came bolted to your new tensioner can have the same soft-groove problem. Swapped the pump pulley on mine and the belt settled in and never moved again.