I've started doing Dagorhir, and one thing I've noticed is that spears have a big disadvantage against anyone armed with a shield. Shields are a lot easier to maneuver than the point of a spear several feet out from the wielder. Thus it's easy for a shieldbearer to block all thrusts and close in without the spearman being able to do anything about it. Since swords and shields and spears were all very popular on the high medieval battlefield, there probably would have been a lot of spear vs sword combat. How would spearmen fight swordsmen?
Additionally, I've noticed it's really damn hard to wield both a shield and a spear. How'd they do it?
Hey, I know your larp!
First, let's establish some historical baselines. Spear and shield was common in the early middle ages, especially in the 5th and 6th centuries. After that, swords gained ground steadily as metallurgy improved and economic ties across Europe + the emergence of more and more professionalized fighters made it easier to get good blades. So let's compare 6th century spears and swords with the boffer versions people use in your game.
In Dagorhir, most people use spears that are on the heavy side compared to the sixth century. In early medieval England, the people who fought with spear and shield used 6' long spears that weighed between 1-1.5lb, and which were balanced to be used in a single hand for loose skirmishing. Compare that to a bandshoppe fiberglass flag pole, the standard spear shaft in Dagorhir--the fiberglass alone weighs near 2lb, and the completed 8' long weapon is nothing like its 6th century counterpart in weight, balance, or length.
In contrast, the swords people use in your game are all far lighter and better balanced than the swords that were used in the early middle ages (when spear and shield was still common). 6th century swords weighed in the neighborhood of 2lb, and they had little distal taper or couterweight. I've held some of the best recreations in the world, and they cut like monsters but are slow to get moving--nothing like a 12oz Dagorhir sword that's counterweighted to swing quick and lively.
So in your game, swords have an advantage over spears that they didn't in the 6th century. Now, as swords became more popular over the centuries, they also got more nimble. Spears, in contrast, got longer and heavier -- think two-handed pikes instead of fencing weapons. The weapons changed to fill different niches. Used for the right purpose, heavy spears work well -- I'm sure you've noticed how devastating spears are in your game when they're used as pikes as part of a massed group of fighters.
So basically, spear and shield worked because the weapons were different when it was popular. That doesn't mean it can't still work in your game, however. If you want to excel with spear and shield in your larp, you need to build a lighter spear, and you need to optimize its balance to make it nimble enough to keep up with the swordsmen. It's possible to do well with this.