A stratmap need not be "strategic" in scope. By that I mean the units being maneuvered need not be at the division or regiment level. I imagine a hex stratmap with each hex being 1-2km across. The units being maneuvered would be battalion/company size, with engagements still taking place with forces at the the company/platoon level as they are today.
Strategically, the player operates at the division CO level, maneuvering infantry battalions, Combat Command task forces, recon companies, HQ companies, etc. Supply lines could come into play as divisional or regimental reserves, replacements, etc are only available if a unit can trace an unbroken line back to HQ. All battalions in a regiment or CC would share the same force pool, so the division CO must make decisions about how to allocate shared resources for each turn. Field artillery could be handled similarly: an artillery company is maneuvered behind the front lines and can fire at a range of several hexes, with each arty company having a fixed number of fire missions per turn. During an engagement, the player can call in a fire mission from the supporting arty company, if there are any available (other engagements may have used them all up!).
Downsides: (1)Increased complexity and game learning curve, but the player could have the option at setup time to designate division and regiment COs as being AI and let the computer maneuver and allocate materiel; the player would then take orders from the brass and fight the company-level engagements as they do today. (2) Hex maps being only 1-2km would require an enormous number of tactical maps to be created. This would only be feasible if this could be substantially done by a computer using online map databases to generate most of the topography; human artists would just review and touch up. (3) Undoubtedly lots of things I did not think of.