Ah, good morning! It’s already spring…? 
Long time no see!
@Kaven: It’s interesting to see how people are still obsessed with the RoF (well, more precisely the RoS), but very rarely, if ever do I see suggestions about the range or the power of the bows. It’s almost as if this became some sort of fashion. Now, don’t get me wrong, I also believe that historically that was an interesting point of bows just as it is nowadays. However, I think that you are mixing up a lot of things regardless of boundary conditions.
The most important is the cultural background. Henry is supposed to be aware of the “western tradition” of archery in the broad terms - well, not even and necessarily that either in the beginning, as he is a blacksmith. I’m more familiar with the steppe bows, but I don’t have any reliable source that states - more importantly, proves - the exquisite shooting rate of the longbowmen. We also don’t talk about two very important aspects of the rate of shooting: How long this elevated rate can be kept up, and how was this practice effect the grand scheme of the battle, like the tactics of the bowmen and resupplying the arrows. Strangely, rather little emphasis is spent on studying logistics when it comes to any battle, really. It’s still a question worth asking that in a half day-long battle what happens after you shot all your arrows in the first two minutes. We know about for example, byzantine sources, but about the clash of two horse archer detachments, naught.
Okay, more tediously:
indian tribes - selfbows aimed at unarmored targets at short distance
ancient egyptians - basic weaponry aimed at limited armor
Kassai Lajos - great sportsman, but admittedly pursuing a career in a sport made up with his own rules. (I quote him: “We don’t follow our ancestors, but we follow what they followed.”) Even if we wanted, we couldn’t do so reliably, since what the resources state about horseback archery is largely a mess. As for my case, we still can’t reliably figure it out whether hungarians in the X. century used thumbrings or not. I also have Kassai’s book right now in front of me, I quote from the section “The bow”: “The average (horse archer at his school) uses 30 lbs bows”, because a stronger bow would hurt one’s body at the practice rate they are doing. Mary Rose says hi! So, again: light bows aimed at unarmored targets at a short distance.
arab and saracen archery - has little to nothing to do with Bohemia.
60 lbs turkish style bow - has little to nothing to do with 130 lbs warbows. Especially with polymer string and injection molded nocks. As experimentally shown, horn and sinew bows don’t really go under 80-90 lbs either, not even early scythian bows. As far as I know, the turks also put a greater emphasis on range, as their competitions show, most notably the “shoot through the Bosporus” one. Mongols did as well, they raised monuments in honor of distance shooters, like for Eshunkei in 1226. I don’t know of any erected for rapid shooting. As for egyptians, Amenhotep II. “founded” a competition by piercing a brass tablet with bow and arrow - again, no rapid shooting.
While I am certainly not stating that the pace of shooting is not an important parameter, putting it above all even at the cost of most other aspects of bow and arrow warfare can easily lead to confirmation bias.
I see you are also familiar with saracen archery. That’s good, it isn’t that good however that everyone seems to cite the “shoot fast”-part, but noone seems to go further. There are also requirements for distance and ballistics as well. These requirements are not the most clear side of the material, but according to Klopsteg, a reasonable assumption is to be able to shoot at a target at a distance of 75 yards / ~70 meters - short ulki - in a way that the arrow will not rise in it’s flight more than 8 feet / ~2,5 meters. In these regards, most people doing “mamluke archery” definitely don’t do mamluke archery. Also, as for accuracy, at this distance the arrows should all group up in a circle with roughly 1 m diameter. The usual speed as far as I know is 3 arrows at a time in the air (releasing the third while the first hits the target), not 3 to 10.
I almost forgot that the “Mamluke handbook” also describes releasing with the thumb finger, which is the method more-or-less used generally in the east, not in the way how the gentleman in the video does it. Scythians also seemed to be familiar with this method, as this statue (~500 BC) from a temple in Aegina shows. By the pattern of your arguments, we could say that Henry should pull his bow with a thumbring. I just showed a historical source for that, after all. 
The data about english archers is indeed “often mentioned”, thereby can easily fall in the “common knowledge” fallacy. I’m still waiting for solid experimental validation. (I often bring up as an example how it was also common and serious knowledge how “bronze armor were useless” after John Coles’ “tests” in 1963) It’s also an issue that while we have some all-over-the-place sources about arrows in the pulling hand, we do not have a lot depicting arrows in the holding hand, not nearly enough to pull conclusions. (László Gyula explicitly writes in his book “Life of the ancient hungarians” - I don’t think it came out in english so I had to translate/butcher the title - that the arrows held by the bow seriously restricts the proper horseback archery. This is by far not an ultimate argument, Kassai himself does exactly that, but I still show it just for the sake of showing that there are counterarguments. Kassai also does not do “military-grade archery”, mostly because of an earlier injury.) In my country, currently the general consensus is that horse archers loaded from quivers, although you can still see some self-proclaimed historians making a christmas tree out of his bow and shooting a good twelve (thin aluminium) arrows in a fast pace. At paint cans. At three meters. Shooting on foot.
I talked about a very arguable expression of “general consensus”, but if you check a number of eastern depictions of the period, be it either about chinese, mongolian, japanese or even egyptian etc., cultures far from each other both in distance and time, you can get the image that the average archer either loaded extremely fast from the quiver, or were not expected to shoot at a very high rate. Or let’s just say that the “boring way” of archery has a metric ton of resources to back it up.
And even at this point, where are we from modeling actual combat scenarios, where the archer is not alone, but a rather frightened, maybe even wounded individual of an army structure? On a battlefield, as a bowman, you are first and foremost expected to incapacitate your foe from a distance of - let’s say - generous 2-300 meters, somewhat less if you are a horse archer. We are in Bohemia in the early XV. century, so chances are your targets will be armoured. In most cases, this is a target you can barely even see. And you are holding a bow that requires 600 Newtons to pull, with arrows weighting almost 80 grams and with a thickness of around 12-13 millimeters. …and your name is Henry, the village blacksmith. Should you shoot out fourty arrows in a minute in this situation, or behave any way a trained mamluke horse archer would ? However, it would be an interesting gameplay mechanics if some form of preparations (for example stabbing arrows in the ground in front of you, which longbowmen apparently did) would reward the player temporarily with elevated RoF, like, I don’t know, 3 seconds per arrow.
And that arrow could still pierce the cranium. After all, that’s the whole point of this archery-thing.