Great idea for a discussion! I play primarily with the 1066 start date for what it's worth as I despise how 867 plays for Christian rulers and tend to prefer playing as a Christian unless I feel like being edgy, so it's the most important consideration for me given I also prefer playing in Western Europe. As it stands, I (currently at least) feel it's best left as is, as I do agree that the game does a terrible job of representing the Norman conquest of England, but on the other hand, I think it's important that an historical start date isn't replaced by alternate history.

I've had a few ideas in the past and some of them have been covered elsewhere, but I've either forgotten the reason(s) it can't be done or I feel it bears repeating or countered, even if not just for myself. Additionally, I'll try to be respectful of your time and the scope of changes you can do as one person. Regardless, here we go in no particular order:

(A. Move the game forward in time to Harold's death/one day after Hastings: I know the character database is a concern first and foremost, but i'd be curious to see how many conflicts or issues there would truly be - it's the span of a month, and I'm unsure how many characters truly will be "incorrect" in some way - surely there's not a load of solidly documented character deaths/title changes in this specific month outside of England? Also, it'd be interesting to see what the error log produces. It's probably quite a bit more work than many people would understand, hence why I'd not take the risk of William's coronation as in CK1 and CK2.

If this one could be made to work, it also has the added benefit of being a cheeky extra scenario, as you could still start the older scenario if you'd rather England stay Saxon (ugh, revolting!)

(B. Cheesy decision/event: This is quite corny and ham fisted, but perhaps preferable to attempting the potential futility of the first suggestion/creating an alternate history scenario. Perhaps a 'simple' decision if you play as William to "capture and kill" Harold; maybe this could be done by triggering the battle events directly, but I'm unsure if the game allows that. I do recall you mentioning triggers being bugged sometimes, in particular one you attempted to do so you could switch England to primogeniture if William conquers it. (ty Paradox, as per)

(C. Whacky date change (bear with me): Inspired by the very same things Paradox does with vanilla, is it perhaps possible to "pretend" the conquest already happened? You'd have to adjust the death dates and other key events (such as title changes) to make it work, and I'm sure there's considerations I'm overlooking due to a severe shortage of modding skills, but basically similar to how pretty much every historical character in the game is set to have been born on January 1st even when the information is easily accessible; basically, we just pretend the conquest happened at some point earlier in the year. If this option is plausible but you have concerns regarding the ahistorical date, I feel it's less of an issue than an entirely fictional scenario, but this is very much a tomato, tomato issue I suppose.

This is all I can think of at the moment, had more but struggling to remember. if I do, I'll add them into the thread. If nothing can really be done at this time, then as stated, I'd personally find it preferable to just leave it as you have it.

I would like to second the "Move the game forward in time" suggestion, except that I suggest instead moving the date to January 1st 1067. This is because, without starting on a very special date like the Battle of Stamford Bridge and focusing on its war, there's no real reason not to just start on the next January first. Furthermore, William the Conqueror's coronation occurred on Christmas Day, so him solidly reigning over England would be a bit more sensible after this point. It'd also mean the start dates are exactly 200 years apart, which would be very aesthetically pleasing.

This wouldn't interfere with the other 1066 wars as the history wars file specifies that both of them continue into 1067. Also, based on a cursory look over the "titles" files, not many titles would actually change hands as a result of this (outside of England of course). Most of the changes in titles (applying to none of the bookmark characters except the kings of England and Norway) in 1066 actually occur before the Stamford Bridge date, so they'd be the same regardless, though there would still be a few (mostly minor) titles changing hands. Of course, you should probably look over the title history files yourself just in case.

One notable change would be that Norway is now ruled by Magnus Haraldson. You may wish to use Olav Haraldson instead since he was more important historically, they were ruling jointly, and Magnus died in about three years while Olav ruled for decades. Whoever you choose, it'd be a good idea to refine their characters a bit, since they'd be major bookmark characters now. As for the "Alternate History" of a continuing Norwegian claim on England, you could maybe have a game start event where the player has the option to justify continuing with Harald's Claim (at a sizable cost since, after all, he lost the war) to regain all of Harald's pressed claims as unpressed claims. The AI, of course, should always decline this decision (unless you can think of a good reason why it shouldn't). Not to mention, Svend the Dane (still alive in 1067) also has a claim on England, so players (and AI this time) will also have the option to press that claim instead.

Thanks for the feedback, guys. It's appreciated!