The more I think it over, the more that John Defilippo makes sense to me.
He comes off that same successful coaching tree. He was part of the braintrust in Philly that won a SB with Nick Foles. While the Minnesota offense hasn't been gang busters, he has maximized the only real talent on that offense (Cousins and the WR duo). He's well connected. He seems to be innovative, but he's experienced-- coaching at some level since 2000, 12 years of NFL level experience, 5 stops as a QB coach, and 2 as an offensive coordinator.
The fly in the ointment here is that neither stop as an OC has been all that impressive. His first in 2015 was in Cleveland, so that context is important. He coached Josh McCown to a 93+ QB Rating there, but overall the offense scored 17 points per game and no running back topped 4 yards per carry.
There was a lot of excited around his arrival with Cousins in Minnesota. However, the scoring offense has been virtually identical to what Shurmur and Keenum produced. However, it should be pointed out that Shurmur was good enough to get a HC gig in his own right, and Keenum had a career year. So matching that production, rather than exceeding it, isn't shameful.
Those are legitimate negatives, but they don't terribly concern me personally. I obviously have my own bias, but as objectively as I can look at it, I don't think that Minny offense has much talent. The top 2 WR's are fantastic, and Cousins is a good QB. But Rudolph isn't a dynamic pass catcher, the OL is bad, and I really don't like Dalvin Cook-- I legitimately think he's bad.
I think the best course would be to hire Defilippo, keep Pettine, and see if Flip can get Zac and Press Taylor out of LA and Philly respectively to be his main lieutenants on offense.