I bypassed mine in a rest area in about five minutes.? Check out the heater hose spaghetti by the firewall in the center.? There are also hoses going to the rear area heater on the floor- I think that they are also meeting there.? ?
Once you get them sorted, disconnect the hoses going through the firewall to the core and connect the feeder to the return (actually don't need to know the flow direction) where there is already a splice tube from the factory.??
Why can't I remember what a "splice tube" is usually called? A coupler?? ?Anyway it's barbed and is in just the right place to solve the problem. Hose may have to kink a bit to contort but that's fine.? ? Should be good forever if you don't care about heat. And anyway, the rear core may still help.?
I eventually pulled my dash and swapped out the core but would not have wanted to pay for all that labor.? Plus the possibility that they get something wrong. Doing it myself, I know how it went and now have practice if not right.? A paid mechanic has incentive to overlook small issues.?
My rear core was later ripped off the underbody by some loose truck tire on the interstate and I sorted that on the shoulder by doubling the hoses and using zip-ties to block them.? Oh well.? I was planning to repurpose that one as supplemental engine cooling so if anybody has a spare, I'm interested.??
Duane