I don't really see that it needs "fixing" at all in the first place.

The -25 morale hit, plus the tactical disadvantage of having to defend the much-hated on-field victory point, already seem ample penalty for being caught in forced-march mode as it is.

Re attritional losses, I don't necessarily see that Forced March has to be imagined as some sort of grinding "death march" at a physically harmful or tiring pace. It wouldn't necessarily impact morale to the point of desertion (as long as the army isn't attacked on the march).

I view Forced March as the army making distance gains each day, rather than marching at a faster pace. The way I visualize all this:

In Normal mode, some skirm/cavalry units would leave first, and main infantry body might wait an hour or two to allow this recon screen to fan forward and out before starting off. Order of march would be close, to facilitate rapid deployment into battle formation. Troops would be fully dressed in armor with weapons readily accessible. The baggage train would be heavily guarded, and the army would move in such a way that the train could always be hidden or maneuvered to safety. The army would stop with several hours of daylight left, in order to set up defensible locations with some minimal palisading, light entrenchment, sentry posts, etc. Indeed, they might stop earlier in the day than they otherwise would, in order to take advantage of favorable ground. Robust sentry presence would be maintained all night, requiring significant proportion of the men awake. All in all, the main body might actually move something like 6-8 hrs during the day, perhaps less during winter.

In Forced March mode, tactical considerations are greatly reduced or perhaps eliminated. The troops wouldn't necessarily march any faster, but could start earlier without having to wait for scouting screen to go out, and could march later into the afternoon or even early evening. They could camp pretty much where they stop, and only need enough time to pitch tents and get some chow before sacking out. Sentry requirements would be greatly reduced (meaning each soldier would get more sleep, compensating for the longer march times). With no tactical considerations to the order, the units could "route-step" (i.e., walk freely with varied gaits) rather than march in step, and the units would string out a little bit. Each individual soldier would still have to carry all of his gear of course, but wouldn't have to wear all the armor, and could perhaps carry it more comfortably. All in all, the army moves much farther each day not by pressing its individual men faster/harder, but rather from de-emphasizing tactical readiness. In this mode, the army could move something like 10-12 hrs during the day.

Heck, the more I describe this, I'm kinda talking myself into hypothesizing that the individual soldier would prefer "Forced March" mode over "Normal". Maybe it's just the implicit connotations of the names that have us tripped up, as "Forced March" just sounds negative. It might be more useful to think of Normal as "Tactical Movement", whereas Forced March is really just "Administrative" or "Non-tactical".

Is any of this historically accurate? I dunno...but it sounds pretty reasonable to me. Viewed from this perspective, it makes perfect sense to me that Forced March carries no particular drawbacks unless the army is attacked, and then the morale/positional penalties are pretty severe.