100% inspired by Crusader Kings 2 I'm somewhat sorry to say, and I suspect we might not have any sources on it. But I'm wondering if any of the Pagan hold outs or kings in Scandinavia tried to 'reform' the older ways as Christianity spread north.
Maybe. But probably not when, where, or how you're thinking, and certainly not how CK2 portrays it.
For those unfamiliar, Crusader Kings 2 allows pagan religions to "reform" their faith into a more traditional religion with it's own doctrines, scriptures, religious leaders, and so on. To do this rules need a certain amount of the faith's holy sites under control as well as a large amount of personal piety (an in game currency that can accumulate and be spent) as well as a nebulous concept of "moral authority" which reflects conversions, priestly power, temples being constructed/raided, and so on. This process is also deliberately taking on aspects of religion familiar to Christians, such as holy texts and priests, to try and stop conversion among the Norse and forge a new religion in opposition to the encroaching monotheists.
In order for any realm to undertake this, especially for the Norse rulers, a large amount of Scandinavia needs to be subjugated by one ruler. This was never really the case in the viking age as no one polity could claim rule over all of Scandinavia and Norse possessions, the closest was Cnut the Great in the 12th century.
But let's get back on topic. Before Christians started gaining a lot of traction in Scandinavia, one Norse ruler does seem to have tried to develop a conspicuous and antique form of paganism. Harold Bluetooth buried his father in a massive burial mound which was unusual for the time, the practice had fallen out of favor some time ago. Anders Winroth proposes that this was an attempt to create a form of conspicuous paganism to contrast with Christianity which started to make inroads at this time, late 10th century, and was associated with the realms in conflict with Harald such as the (Holy) Roman Empire. By deliberately appealing to ancient pagan practices it's possible that Harald was trying to create a new form of paganism to contrast with his southern rivals and shore up his support at home.
If this was his original intent, it ended up an abject failure as Harald converted to Christianity scarecly a decade later, and he even dug out his father and reburied him in a church. Following his conversion Christianity took to Denmark rather quickly and Norway soon after, Sweden took a little longer but followed suit as well.