Aha.
This one? Looks like it would be a good find.
Now that I've thought about it a bit more, I can add the following: my first issue with the strategy board is that - while simple is good - too simple denies the possibility for unique situations to form within the game. I am a very bad chess player, but if there is any part of the game that I love the most, it would be the middle of the game when the board is one big mess and the pieces are all in odd positions. Even though the rules of the game haven't changed, that type of messiness is where the real strategic challenge of the game shines through since you can really appreciate - and use - the complexities. Compared to the beginning, when all the pieces are in the same positions and the number of obvious moves are already known, against the end of the game when too few pieces are left and it becomes a rather robotic chase remains on the board, the middle of the game is where the real fun part is found. This is what I meant for getting "out of book."
In my
old strategy game from last year, I designed it with the imperative to get to this "messy" state as quickly as possible. However, the tradeoff for it became obvious: the usual playtime of a single game went from 2 hours to 10 minutes. Good for replay value and multiple matches, where if you win you win and if you lose it's not that big of a deal, but: the shorter and easier a game becomes the less ultimate satisfaction is gained from winning.
When it comes to the action, I'm afraid there really isn't that much you can do with single-button gameplay. The most you could do with that is a one-two-three tapping combo, a running/dashing attack, or probably include a form of charge attack - similar to the Spur from Cave Story. Other than that, you may also need to make the stats and attributes of the game pieces more on display. For example, that archer might have a very long range attack, but it would be comparatively weak against a scythe to the face, and a footsoldier may have more HP than one of those ranged spellcaster types.
If you take the option for the charge attacks, you may want to have them customizable on the map screen during a player's turn. You'll want to have this as adjustable as possible. Let's say a player can make a unit's Level 0 (base) attack just a swing of their sword, their Level 1 (small charge) might be a ranged boomerang throw, and their Level 2 attack might be a close-quarters Zelda-style spin attack. The penalty for changing a unit's attack style would need to be skipping a movement or attack phase for a turn. The selection of attack styles will likely need to be limited to the quality of items that the army has, so if a spellcaster gets his fireballing tactics from a magical cuneiform tablet, he may have a level 0, level 1, and level 2 charge, but not a level 3 or up because the item quality isn't good enough.
One thing that may be necessary is having longer player turns, and the ability to use/move/attack multiple units. You'll need some way of figuring out, so moving or attacking with two strong units with lots of items equipped with be the same as moving five weaker units. Maybe a simple "movement cost" stat could be introduced? With it, you can safely include unit types that lean more towards supportive ability rather than offense, providing healing or status buffs.
I don't know if you have this already, since it didn't come up in my playthroughs as a make-or-break issue, but you'll need to make sure that the stats remain consistent for each unit. So if a footsoldier won on the last turn, but took some damage, that same amount of remaining HP will carry over into its next battle. I think you already do have this, but if you make that sort of information on display in the map screen, the amount of strategy the game requires will rise dramatically.
The size of the arena is another issue. The way it is set up right now, the arena is so large that the weakest units are the ones with the worst attack range, regardless of how powerful they may be. If you want to utilize more close-quarters combat -
as ancient battles used to be before the invention of proper ammunition - then you'll need to make the arenas much smaller in size, and have the units engage each other at closer distances.
In fact, if you include HP, Offense, and Defense as base stats, other stats may include: speed (in arena movement speed), movement (how far they may travel on the map screen), stealth (how close the unit begins a battle to the enemy unit when it engages), and evasiveness (how far away the unit begins a battle when engaged by another player, with the two stats evening each out). Then there are other stats of a more standard fare, like critical hit chance, chance to dodge or "miss" an attack strike, as well as the ability to gain passive bonuses.
The terrain of the battlefield is another issue. You'll need to make it so that a player can retreat from an engagement if necessary. The best way to do this would be having the player "run into" the arena edge for some amount of time before the battle ends and they scuttle onto the adjacent map space in the direction that they ran (provided there is not another unit already there). Another helpful detail would be directional placement: if a unit engages another unit from the north, it would appear on the arena as to the north of the opposite unit. Other things to include would be more level-based items and gimmicks, like parts of the stage that the players can interact with to some possible effect, or cause a chain-reaction. Cutting down a tall tree to land on the opponent, or maybe using a knockback-inducing attack to push a nonflying opponent over a pool of fire. Granted, if all this were to be included, the player would need to have some way of knowing what type of battlefield a particular area has before engaging. Maybe a player can inspect the type of terrain a particular part of the battlefield has if one of its units is in movement distance of it?
Whelp, terribly sorry for writing such a long post -- I didn't have the time to write a short one. Nonetheless, I hope some of this can inform your design choices.