Using the pay to succeed mechanism in war games.

Don't make it exp at all, in a war game. Make it military spending.

Maybe each player starts with $10m (or whatever units are appropriate), and gets $1m per turn. Then you can spend in $1m increments similar to what you have for exp. If you run out of cash, too bad.. should've saved some for an emergency.

(obviously you could also gain cash other ways, if that enhances your design)

Completely just realized @let-off studios already mentioned commanders. I currently see no problem with the limited mobility of Commanders. Isn't that the point? What exactly is the problem with that? I think the entire advantage of using Commanders to track EXP is that they stop you from being able to "farm" EXP one place and use it in another. That seemed to be the main problem in question.
I, personally, don't see the problem, but maybe you could explain.

This reminded me of the mechanics of Star Wars: Rebellion. At the beginning of each round, the two players alternate placing Leaders around the map, either to take part in missions or to lead armies. Perhaps you could be inspired by how they do it, but I'm not sure how much there is to take from there.
Experience makes a little more sense than Karma, I would say. Experience is gained by winning and losing battles. Karma isn't exactly a tangible, or even real, thing. To include it in a wargame might seem a little out of place compared to Experience.

I agree with @let-off studios.
Here are the problems with limiting XP spending to 1:
-Lack of advantage as you accumulate XP. The only advantage to more XP is a longer lasting advantage.
-It's the same amount you gain when you lose a battle. There is no way to decrease XP gain, as the minimum is 1. Perhaps this could be fixed by making you need to pay 2 XP for +1 to the die roll.
-All Commanders give basically the same advantage. If XP is tracked by commander, it wouldn't matter much which commander you put where, as long as they have at least 1 XP.
-Again, it doesn't have a huge effect on the outcome of the battle; it's basically paying to win ties. Even then, though, the defender could just pay as well, nullifying your advantage. In other words, it's too easy to nullify the effect of XP.

Now you pointed out something interesting with XP. It's true that it doesn't really work in the way that I and yourself have conceived. However, I had an idea.
What if Commanders have the ability to level up? I realize this makes it even more tedious to track individual Commanders, but this might fix the problem.
A Commander starts out with an XP cap. Once they acquire that much XP, they can gain no more. However, every time a Commander wins a battle, they level up, increasing their XP cap and allowing them to theoretically be more helpful in battles. This may lead to a form of "steamrolling", where a Commander wins battle after battle, leveling up over and over, but they still need to spend XP to provide any advantage in a battle, so likely after a battle or two, they will have no more XP left.
Another problem is that a player may try to accumulate Commanders in one space, so that when they win a battle, all of them level up at once. This could easily be solved by limiting it to 1 Commander per space, or something along those lines.

You're absolutely correct. It could lead to a snowball effect, yes. That is a big problem.
Morale instead of XP is an interesting idea, but hard to implement with the same rules as we've established.
Experience, alongside the Commander thing, is a fairly solid idea, but has many kinks.
I just had an idea.
What about Supplies as a resource? When you're defending, you might need ammunition, food, sandbags, etc.
The more you have of that, the longer you can survive an attack. What if armies could sacrifice "Supplies" as the resource that allows them to automatically win defenses?
The problem with this is that it still can't be tracked on a global scale, so you would still need to track it by the space. It could lead to interesting "supply line" mechanics, but I'm not sure how well this would fit into the preexisting ruleset.
Another idea: What if the attackers attack, roll their dice, and announce how many Supplies they are going to use to give themselves an advantage. This represents how much ammunition/fuel/food they decided to bring with them when they attacked. The defender can then decide, after rolling his dice, based on the total attack strength of the attacking force, whether he wants to accept the defeat, or spend Supplies to win the battle.
Some problems with this:
-It turns the game into a very statistical and analytical game, unless you instead use an "auction" system where the attacker and defender one up each other by upping the amount of Supplies they will sacrifice. More on this mechanic later; I just had a brain wave relating to it.
-Unless Supplies are somehow kept hidden to the enemy player, one side can roll their die, then make their decision based on how much Supply the enemy side has as to whether they want to try for a victory or just "throw" the battle. One possible fix for this is to make the attacker choose how much Supply they want to bring in the attack before they roll their dice.
-This may lead to many "cold war" situations. Perhaps a way to fix this would be "artillery bombards" that destroy enemy Supplies, or a cap on how many Supplies can be in one space. As another idea, it might fix this problem if the attacker, when they lose, does not lose all of their Supplies; the Supply lost by attacking is capped at 1, to encourage larger scale attacks.

Now, about the "auction" mechanic. This only works if neither side knows how much Supply the opponent has. This can be accomplished through upside down tokens with different amounts on them. This allows the opponent to have a vague idea of how well Supplied the enemy is (you could call this the opponent doing a flyover over enemy territory, seeing the warehouses, and making a vague guess without knowing how fully stocked the warehouses are).
A battle would start with a roll of dice. Then, starting with the side with the smaller number, players take turns upping the amount they're willing to spend, with the cap being their total Supply plus the number on their die. As soon as one player passes, the "auction" for victory ends, and the side that bade the higher number wins.
The last step is to subtract Supply from both sides. Each side loses Supply equal to the number they bade, minus their die roll.
As an example:
Player 1 (P1) attacks. They roll a '4'. The defender (P2) rolls a '5'.
P1 has 6 Supply. P2 has 4 Supply.
P1 starts the bid with "6!"
P2, having a good amount of Supply, can bid back with "7!"
P1 has plenty more Supply, and bids, "8!"
P2 is hesitant. With one Supply remaining, they have to hope that they can win the bid with "9!"
P1 becomes just as hesitant. If they use their last Supply, they will be defenseless against further attacks. But they push on anyway. "10!"
P2 has no more Supply, and bails. P1 has won!
Now for the cost. P1 bade 10 - 4 = 6 Supply. P2 bade 9 - 5 = 4 Supply. Both P1 and P2 lose all their Supply!
Now, a real battle may not result in complete loss of Supply on both ends. Depending on how expensive you make Supply, a typical battle might look different.
Consider all of these as suggestions, for your own benefit. I just threw all my thoughts down in the hopes that you might be able to use some.

In traditional war games airbases often have to trace supply line like Ground units.

World War Two naval units often have logistics represented by range of ship. I.O.W how far it can go on a full tank of Fuel.