Just an example planet I shat out in Paint.net. It's a single continent reaching from one pole to the other. You probably don't even need a map at first, a featureless plain is fine too.
First suggestion: Ditch the zones. Use strategic points instead, mirroring star systems on the strategic map, in a way. Here I mostly used towns and military bases, but on less populated planets those would be passes, land bridges, mountains, places relatively safe from orbital bombardement etc. Some points give boni, better defense, reinforcements, better anti-air/space capacities etc.
Connect them with similiar code to the starmap one. That's important, because battles will be about those routes and those points. I treated the oceans as impassable in this mockup, but that's probably too complicated for the alpha.
Now, armies can capture those points by moving into them. Either over the routes, or by landing from space... which is only possible in some locations. They automatically leave appropriate garrisons when moving on.
One could mark captured territory, eg by marking the polygons formed by the points in the color of the majority of the adjacent strategic points... but that would be complicated and a bit pointless. The territory itself is useless (mechanically), it's all about the points and the routes.
What's important though, given how the IG works, is the Front. If you hold a point connected to an enemy point, you have two options: Defend and advance. The second one is the standard choice, because you won't win many wars by sitting in one spot. If both parties advance, the route is contested.
It's cosmetic, but if nearby routes are contested, it would be nice to connect the individual frontlines to a single, large one. It could be even mechanically important if you can shift forces along that larger front. Anyway, those circles are forces holding a certain part of the line. You can check them out("Infantry: 423th Cadian, Elements of 612th Krieg Pioneers. Vehicles: Valhallan 12th field artillery...") and switch them between different aggressive or defensive "stances": "Entrench!" gives a small cumulative bonus every turn, "Hold the Line!" i.e. expecting an enemy attack, gives a somewhat bigger one that does not increase, "Charge" is an aggressive attack with high danger of entering melee etc. etc. What kind of troops and equipment you have in place can make drastic differences in how effective a stance is, and how well enemy attacks are handled.
Armies 1 through 4 are involved in (presumably static) warfare, 5 is heading for a strategic points your scouts think is undefended, 6 is some kind of recon team or partisans behind enemy lines, either just collecting intel or getting ready to ambush E.
Here Hive II is held by Blue, who either decided to defend it or had to retreat into it after losing the battle for the routes, and now is under siege by Green. That probably negates most of the boni holding that strategic point usually grants, and traps your troops there as long as the siege lasts. But I'll assume a Hive city is a good place to defend, mostly because it must be a nightmare to attack.