My trouble is that we want as close to "by the book" as possible, while I myself still want to try something new. My trouble is the cleric class specifically is modeled after a monotheistic crusader archetype, and the most Immediate answer for how to change that is already supplied - the Druid class.
I'm inclined to disagree with that assessment of the Druid class. The Druid class has a very limited relationship to anything but itself, and while it's got amazing creativity and thought put into it, it really isn't modeled on anything. We know virtually nothing about the real Druid of history, but one thing we can be certain of is that it had nothing to do with the Druid of D&D at all. We don't know even to what extent the Druid was an animistic priest or a polytheistic one. We know nothing of their rituals or beliefs. Virtually everything that people think they know about the Druids - mistletoe, holly, sickles, long beards, astronomy, nature loving, robes, etc. - is entirely a whole cloth invention by various writers with various agendas in the 15th century and even the 19th century. The 'Druid' as a fantasy role-playing class has become its own archetype based on the Druid, in the same way that the Ranger as a fantasy role-playing class is only barely based on its inspiration in the Lord of the Rings (Aragorn for example never uses a bow at any point in the books) and is instead now mostly self-referentially based on itself.
I am uncertain what exactly you are trying to model. You seem hung up on flavor requirements, yet you don't seem to be bothered by Brigid, Balder, or Wotan being worshiped by Great Druids who have to fight to assume the position, can shape change into animals, and who hold mistletoe to be sacred and use it all their rites while wielding sickles and Egyptian kopesh. If you really feel the need to closely mechanically model individual priesthoods, you'll have to use something like the specialty priesthood mechanics of 2e and roll your own class(es). Or you could use the 1e class as is, and just roll your own flavor. In 3e, I tend to use the Green Ronin shaman class in the roles you seem to be focused on, and it would be a bit of work to back port it to 1e but there is a lot of compatibility to between the two in the spell lists and its basically a straight port.
I've considered modeling them as Goði, or Vittan, or even as shamans, but I can't come up with a happy medium that my players will digest.
Honestly, if you are doing northwestern Europeans, you'd probably model a lot of them as Bards.... though granted, the Bard itself has taken on a life of its own and its no longer well grounded in the inspiration of the Kalevala.
- how would turn undead be handled for these clerics?
Just as is. Undead are evil spirits and the clerics naturally have the ability to rebuke them because of the knowledge that they have of spiritual matters. Exorcism is not a uniquely Christian concept, and indeed, compared to animistic religions its not even a central rite.
how would the notion of a knightly order be handled?
Ignored in most cases, and expanded to include something other than the high middle ages concept of what it means to be a knight where applicable. For example, what does a 'knight' look like in 4th century Sweden, shorn of its southern European romantic high medieval notions? It's a low born warrior mercenary, akin more to the notion of bandit than the plate mail wearing crusader of Hollywood or concensus fantasy.
how do I maintain the cleric as a devotee of some otherworldly power?
By understanding that the role of an animistic cleric, even as devotee, is different than the monotheistic conception. In this case, 'devotee' can mean things like 'vassal', 'ally', 'employee', or even 'customer'. The priest performs rituals that appease or please some otherworldly power in exchange for power and favors. It's less a matter of serving as it is a matter of buying things from the diety. Thus, you might not even like the diety you are nominally associated with. It may simply be that it doesn't rain unless you give the deity his yearly human sacrifice, and the kidneys of six spring lambs, and a jug of wine every year and for the good of the community well that's what you do. Meanwhile you aren't in an exclusive relationship. Polytheism is just that, and by monotheistic conceptions, its promiscuous in its worship. You go ahead and worship the god in a particular oak tree (a dryad?) if that gets you what you want. Polytheistic gods aren't typically 'jealous' so long as they get what they want. Indeed, there may be an assumption that you worship all of the gods to prevent one from being jealous and offended by you paying special attention to another one. You end up with a long list of things you must do to keep everyone happy, petty spiteful things that gods tend to be.
