Your research might benefit from clarified terms. "Hit and run" is very different from "fire and maneuver." I suspect that you're actually referring to "line infantry tactics."
"Hit and run" means to execute an attack and then leave. There are typically two possible objectives for hit-and-run tactics, one is to allow a smaller force to deliver a targeted, decisive blow to a larger force, by surprising them and then retreating before the larger force can mount a counter attack. It's important to know that this always has a very specific target (the radio tower, the ammunition supply, their only tank, etc.). Once that target is destroyed, the attacking force GTFO.
The other goal is to distract a larger force by mounting a feigned assault, and then retreating. The retreat involves mostly running, with little or no covering fire. The success of the retreat relies on timing, i.e. withdrawing before the other force can effectively respond.
"Fire and maneuver" means to use part of your force to fire on the enemy while another part of your force moves into a better position. Overwhelmingly, this is an attacking strategy, not a retreating strategy, although Navy SEALs and other elite forces use a "center peel" to disengage from an engagement they can't win (key word disengage). Most commonly, a "fire element" forces the enemy to remain hidden by shooting at them, while the "maneuver element" takes the opportunity to move to another position, where the enemy's hiding place doesn't provide enough protection (usually from the side/flank). This is a strategy employed by fireteams (4-5 men) or platoons (15-20 men), but rarely by groups larger than that.
Also keep in mind that the side that is advancing always wins. Wars are not fought over people, they're fought over places. It doesn't matter whether I kill all of your men, or just run them out of town, I still took the town and that's the real win. Consequently, there's not any real strategy to retreating ahead of your enemy while you pick them off behind you. If they're losing people, they'll just stop following you. If you're small enough, they'll outflank you and force you into a position where you can't get away, and then they'll wipe you out.
Finally, what you're describing is I think inspired by "Line Infantry," but there is no line infantry method that involves falling back. With "Fire-by-rank" a rank would step forward to fire, and then file off to reload. "Salvee" meant basically everyone fired at once, and then charged with bayonets. "Swedes Way" provided perhaps the most opportunity to retreat in an orderly fashion, but that's not a winning strategy, merely a controlled route.
The two most successful strategies would likely be to surprise the larger force, hoping for a quick win, or quickly closing to melee range so that bows become useless. Generally, in "asymmetric warfare' like this, the smaller force prefers guerrilla tactics, which involve lots and lots and lots of very small non-losses. They never win, but they also don't lose.
It's worth noting, as has been discussed briefly in the comments, the difference between the tactical and the strategic. The example provided was the strategic success of the Russians against both the Napoleonic campaign and the German campaign. The maneuvers discussed above are tactical maneuvers, meaning they are "low level" both in terms of who needs to understand the behaviors (individual soldiers), and the goals they are meant to accomplish (winning this battle right now). Tactical elements (units, maneuvers, decisions) are those that are designed to determine the outcome of a particular engagement. Strategic elements are those that are designed to accomplish big-picture goals, and frankly have little to do with the particular tactics employed by individual units.
Even in the odd case of the Russian campaigns, the rule still holds true "The advancing side always wins." The Russians won because Napoleon and in turn the Germans could no longer afford to advance. Russia lost every (yes, with qualifiers) engagement because Napoleon and the Germans advanced through whatever territory was in dispute. Once they stopped advancing, they stopped winning. Perhaps the best-known examples of Sun Tzu's rule "Good strategy with poor tactics is the slowest path to victory, but poor strategy means certain defeat, even with good tactics."
HOWEVER, it might be fun to create an army that deliberately exploits this well-known rule of warfare, by specifically practicing a "feigned retreat" during which they specifically pretend to route in order to draw the enemy into a trap. Something like an extreme version of a Pincer Maneuver. Again, this has to be carefully employed because as pointed out above, if you're running away then I'll just stay here and keep the buildings, territory, equipment, supplies, civilians, or supporters you left behind.