So, my point is not to argue whether the archery is suitable for this game, but instead to talk about various mechanics it could exploit.
It would be absurd if largely outdoor Sui Generis doesn't end up with archery. And I certainly hope SG lets you look up just to enjoy the sweeping vistas, besides this being useful for long-range shooting. But all that's a problem for another day. Exanima is a different animal.
If you want to discuss the mechanics of trying to use bows (and other missile weapons) in close combat, you first have to forget all the BS circus "archery" in all the other games you've ever played and fantasy movies you've ever watched. Then you have to force yourself to remember how it works in real life. And when you do that, you'll realize that not having archery in Exanima is no big deal, the game can easily do without it, but thrown weapons are a great lack.
So, real life stuff:
With bows powerful enough to use in war, you're not going to be able to shoot and move at the same time. You need your whole body to draw the bow, based on feet firmly planted. And you're not going to hold the bow drawn for anything more than an instant, either. First, it's very, very difficult physically just from the strength POV, again requiring feet firmly planted. Natural bows follow the spring force law, requiring more force the further you draw them. Second, it's very bad for bows to be held drawn---it damages the wood fibers, causes the staff to take a set, and reduces both power and lifespan. Even being just strung with no draw on them at all is damaging, which is why bows aren't stored strung, let alone drawn.
Assuming the character has already strung his bow (not a quick or easy task), therefore, a realistic firing mechanic would be walking around with an arrow nocked and pointing mostly down, left index finger looped over the arrow to hold it against the side of the bow. Then, when you want to shoot, you stop, plant your feet so you're lined up to shoot in the direction of the target, and guesstimate the elevation needed for the range to the target. At this point, you raise the bow to the desired elevation while simultaneously drawing it, which is what enables you to get your whole body into the draw. The bow reaches full draw at the same time the arrow reaches the desired elevation and you immediately release the bowstring. No holding the bow drawn. Because the whole drawing and firing thing is one smooth, combined, continuous motion, there is no need for any sort of stamina meter or whatever, which is totally unrealistic.
So that's getting 1 shot off. Now you have to reload. This is a 2-step process. First, you have to get an arrow from somewhere and hold it in your hand. Second, you have to orient the arrow correctly on all 6 axes so you can nock it. Let's look at each step.
First, getting an arrow in your hand. If the arrow comes from a quiver, this isn't a fast process, especially if the arrowhead is barbed. But regardless of arrowhead, you need to do it smoothly and carefully so as not to damage the quiver, this arrow, or any of the others in the quiver. It's very easy to screw up the fletching feathers with clumsy, blind groping and that means the arrows won't shoot straight. So this will take several seconds and is best done standing still or walking slowly so the quiver and its contents aren't bouncing around very much.
Now nocking. When the arrow leaves the quiver, it's not pointed in anything like the correct orientation and is also on the wrong side of the bow. So now you have to bring the arrow around the bow while rotating it to point the correct direction and bringing into contact with the side of the bow and the bowstring. That's the easy part and can be done fairly quickly. But somewhere along the line, you also have to roll the arrow so the nock lines up with the bowstring and the cock feather points away from the bow, then actually fit the nock on the string. This rolling can be done by feel with the proper type of nock, but usually you have to look at what you're doing and you always have to pay attention. So this part of the process also limits what else you can be doing at the same time.
So all in all, quivers (at least when on your back as opposed to hanging on your saddle in front of you) contrary to games and movies, aren't really quick-draw devices. The way to get a high rate of fire with a bow when on foot is to not use a quiver. Instead, you stick the arrows in the ground in front of you, already rolled so the nock and cock feather are oriented mostly correctly. Then you just stoop slightly, pluck an arrow from the ground, fit it to the bow almost instantly, and then do the continuous draw/aim/fire motion as you come back up, repeat. Problem is, the preparation for this is time-consuming, once done you can't move at all without leaving your ammo behind, and you need dirt under you instead of the stone floor of a dungeon. Also, all your shots would be in essentially the same direction. IOW, this is a battlefield option, not a hunting or adventuring option.
Bottom line, therefore, is that in the dungeon, you'd probably only get off 1 shot every 10-15 seconds and be unable to move much between shots. Given that the enemy can cross the visible distance in less time than this, it's unlikely you'll have a chance to fire more than 1 shot per battle anyway, unless the AI is totally braindead. And then the enemy is in your face while you're still holding the useless bow with 1 hand and fumbling in your quiver with the other. Which is why bows weren't used much in close combat historically.
Thrown weapons, however, have a long history of close-combat use. Throw 1 or 2 objects (Roman pilum, Frankish axe, Aztec atlatl darts, beer bottles in bars, etc.) as you close with the enemy then hack and slash. Or, in a later era, fire your muzzleloading pistol once and then use it as a club to compliment your sword. Or fire your musket and charge home with the bayonet. Such weapons can be used on the move and don't get in the way of your melee weapons, or can even be used in melee. The battle is still decided by melee, the thrown/fired weapons just improve your odds before you come to blows.