It's amazing that no one has done a King Arthur (Tudor) timeline here before! Maybe the possibility is so obvious that no one actually got around to doing one.
Please don't rush headlong into the future - as a Tudor era fan, I'd really love to see this more fully textured. Anyway, every alt-hist ends up effectively being a parallel history, the distinctive qualities of the POD being lost in the ripples of time. (That is, by about 1700 or so this TL would have much the flavor of any timeline with a 16th c. POD.)
There are so many things I'd love to know, like what becomes of Anne Boleyn - married to Derby, married to Wyatt, the Archbishop's discreet mistress ... the possibilities are legion. And a host of similar questions.
A few specific comments and some grumps.
Arthur's love of archery - you mention it right after he survives the sickness that killed him in OTL. I wouldn't expect huge historical consequences, but it could have some interesting small ones. It could get him in a jam, if he thinks he can win with Agincourt tactics - those days were past - or it could put him in the forefront of bulking up his army with arquebuses.
For 1513 you mention de Foix, in Italy, capitalizing on mistakes by Arthur. Do you mean that Arthur was campaigning in Italy? That seems awfully unlikely.
I agree with whoever suggested having only a ceremonial capital at Winchester. Kings still moved around a lot, and Arthur might well build a palace there, but moving the seat of real government from London at this late date seems unlikely. If he ignores my advice and does it anyway, it could have consequences downstream - parallel to the price the French monarchy paid by moving to Versailles: losing their touch on the pulse of the realm's main city.
Nice irony that ATL Henry VIII becomes fully as anti-protestant as the OTL one was (till it suited his interest to reverse field). But there was very little English protestantism to suppress in OTL 1524, and wouldn't be much more in this TL - in fact, "protestantism" did not really exist yet. Of course there was heresy, and the stake to deal with it, but the lines between reform and outright break were still quite hazy compared to even a decade later.
I'm with the Pasha - a successful crusade to the Holy Land, right at the peak of Ottoman power, pretty much rings up "no sale" with me.
They wouldn't head for the Holy Land anyway; they'd head for Constantinople to strike at the head of the beast ... and probably get their own handed to them.
Does Arthur build up the English navy, as Henry did in OTL? Pettifogging point, but "HMS King Arthur" is anachronistic. The usage HMS didn't come in till much later, and the ship would have been
Arthur Royal or some such.
A colony in OTL New England also seems very unlikely at this date, at least in the familiar sense of American colonies. The population of England roughly doubled in the 16th century - in the 1530s and 40s there wasn't the population pressure to cause colonization. A fortified trading post would be possible, but very unlikely a colony in the sense we know.
Even a trading post should be either farther north - the St. Laurent - or farther south, like maybe the Hudson. Major rivers going into the interior, suited to the fur trade. Boston just has nothing going for it in 16th century eyes.
Finally, Hannah sounds all wrong - Elizabeth, Katherine, Jane, anything but Hannah! The problem is that to OTL ears - and OTL is where we're reading this
- "Hannah" has a very distinctively Protestant, specifically Puritan flavor. Apart from the long-established standbys, like Elizabeth and Mary, they were the ones who popularized a lot of Biblical given names. I could be wrong, but I'd be very surprised if anyone in early 16th c. England was named Hannah, and for a princess at that time it sounds all wrong.
All of this is basically quibbles, but I'd seriously love to see this TL filled in and developed for the first half of the 16th century rather than just rushing on to later eras. But then I'm a Tudor junkie.
-- Rick