While the parts themselves can be replicated using medieval tech they have nothing to do with a bow's maximum velocity.
Where maximum velocity comes from:
Your materials have various properties depending on if they are in the belly or backing of the bow that determine it's snap. More snap means a higher base acceleration. Wooden bows tend to have a lower snap than something like fiberglass; so, medieval archers compensated for this with arm length. This works up to a certain scale because the snap is compounded across the length of the arm. Arm length compounded with materials determines the ideal maximum velocity.
What about draw weight and length?
These are important factors behind a bow's power but not speed. A bow with a lower draw weight will receive more relative resistance from the weight of your arrow meaning a bow with a higher draw weight can more effectively fire a heavy arrow, and will shoot a little bit faster because it can better overcome the arrow's inertia, but still caps out based on the material limitations. It's like this: a strong man can not throw tennis ball much faster or farther than a weaker man with similar technique, but a strong man can throw a bowling ball much faster and farther because he can overcome the weight better.
Medieval war arrows were on average 2-3 times heavier than hunting arrows so they could better penetrate armor which is why draw weight was so important on a warbow.
Draw-length is similar to draw weight in that it mostly contributes to doing a better job of reaching the maximum velocity that your snap allows. A greater draw length gives you more time to accelerate the arrow allowing you to reach closer to your ideal maximum velocity before it leaves the bow, but again, does nothing to increase the ideal maximum velocity.
What does a compound design do?
A compound design uses pulleys to convert poundage into draw length. So, if you have a crossbow arm with a 200lb 18" draw, and you compound it by a factor of 2 (that is a single wrap on each cam), then you reduce your draw weight to 100lb and extend the stroke to 36". Although this gives you the same specs on paper as a standard warbow, your bow tips don't have to move as far as they would if it was a warbow giving you a higher apparent snap. So your arrow is shot at a higher speed and lower power using the same materials.
The issue when it comes to making compound crossbows out of traditional materials like wood is that wood performs much better when you thin it out more. The thicker you make your bow arm, the greater the backing tension and belly compression becomes as you apply a given amount of draw weight. Furthermore, crossbows become MUCH more cumbersome than warbows if made as long as a warbow. Warbows and war crossbows are designed to be used in battle formations meaning that you can make vertically aligned bows much longer than horizontal ones without getting in the way of the guy next to you. For this reason, war crossbows were typically no wider than 25" whereas a warbow was typically 72". All that extra length gives you more material to store potential energy before your wood ruptures. So, while you could make a compound wooden crossbow, you could not effectively make it at a scale that would be as strong as a warbow.
So where does this leave you?
Since the viking age mostly predates spring steel, fiberglass, etc, the fastest bows you can really achieve will probably be just over 200 FPS using either a bamboo and hardwood composite or a horn and sinew composite. Neither of these materials would particularly benefit from the compound bow or reverse draw crossbow design. Compound bows need to take advantage of modern materials that can store much more potential energy than traditional materials. Traditional materials can already be pushed to thier limits without a mechanical advantage, but steel and fiberglass when coupled with pulleys can get a better effective snap than wood without having to sacrifice too much draw weight or flexibility.
The reason for reverse draw crossbows is because those same materials have more snap in the compresion state than the tension state. In contrast, most traditional materials get more of thier driving force from the tension of the backing material than the compression of the belly material; so, inverting them to be compression dominate would make them worse.
If you want a better projectile speed/range, the Roman manuballista and scorpions could hit speeds much closer to a modern crossbow using coiled sinew cords. These designs don't work on the principle of tensing thier arms at all; so, reverse draw mechanisms would not apply, but you could in theory add a compound bow mechanism to one to multiply it's speed in exchange for a lighter projectile. Vikings could almost definitely make them if they tried, but they were really heavy weapons compared to bows or crossbows; so, the trade-off is only worth it in certain cases.
If you fast forward to the later medieval era though, you will see spring steel crossbows start coming into play. These were limited to very short draw lengths because the arms could not bend much, but they had tons of snap and draw weight. If you were to add compound or reverse draw mechanisms to these, then you would be able to achieve something much closer to a modern crossbow without having to make something too heavy. That said, spring steel was never an easy thing to make, even in the late medieval period, it took a highly experienced smith to properly temper the steel without the use of modern high temperature thermometers.