I quote from the rule “Final Battle”

As a Daily Action, the Allfather may announce that a Skirmish has taken place as part of the Final Battle.

A Skirmish is announced by first rolling DICEX in the GNDT, where “X” is the number of numerical Einherjar Statistics, and where the roll has a comment of “Skirmish Check”. The number rolled shall be used to determine which of the numerical Einherjar Statistics is relevant to the Skirmish, by counting down from the top of the list in the “Statistics” rule - this Statistic is the “Challenged” Statistic.

Each Valkyrie who has recruited one or more Einherjar shall then have their Skirmish Ratings calculated - this is the total of the Challenged Statistics for each of that Valkyrie’s Einherjar.

The single Valkyrie with the highest Skirmish Rating (if one exists) is triumphant, and receives 10 Acorns. The single Einherjar with the lowest value for the Challenged Statistic (if one exists) has fallen, and is removed from the Einherjar page.

After having calculated these results and made the changes required, the Allfather should post a blog entry summarising them, and also describing the opponent that the Einherjar faced.

The statistic “Tinkering” is ignored for purposes of Skirmishes.

So the way this works is, Skirmish Ratings are determined, then the highest one wins.  That kind of takes some of the drama out of it.
I would propose having Skirmish Ratings equate into a number of dice (say, DICE4) that are rolled, then the highest aggregate roll result wins.  (If the Skirmish Rating is less than zero, then you roll a number of dice equal to the absolute value of the rating, but subtract 2 from each result).  That way, if the relevant statistic is, say, Combat, then someone with a Combat +8 doesn’t necessarily always win over someone with a Combat +5.  More likely than not, but not guaranteed.  This way someone with a negative rating could also still win the skirmish in theory.
Before I propose something like this (not that I’d be offended if someone else takes a crack at it first), I’d like to get a sense of what the numbers should be: does xDICE4 (where X = Skirmish Rating) sound good?  Does ((xDICE4) - 2x)  for negative skirmish ratings sound good?
We could also have Skirmishes involve, say, up to two or three different statistics at the same time (say, Combat + Wit + Charisma).
I’m also considering a proposal to add a new “GLORY” figure tracked for each Valkyrie in the GNDT.  Everyone starts at 0; Glory is earned through winning Skirmishes; Victory condition involves amassing Glory; perhaps a Dishonorable Einherjar who wins a Skirmish earns less Glory than an Honorable one.  Any interest?