Why don't you try not using miniatures? Is it really that much of a requirement that your combats be mapped out with miniatures for everyone? I'm just curious, since all my experience has shown me that maps and models slows a game down to a crawl, and makes it closer to a TT wargame than a roleplay game (since you can see where enemies are on the map, when your character possibly doesn't know they're there, etc).
It's hard for some people not to jump to extremes. They hear "gridless combat" and "abstract <anything because they've already begun breathing into a paper sack with a panic attack>" and immediately jump to "massive melee in a complex battlefield where no one knows what range they are and Edgar has just fallen asleep in his bowl of doritos."
Very few people consider the middle way of using a map and placeholders (minis, popcorn, beads, push pins, a marker dot, a finger) to keep everyone up to date with spatial locations of various combat participants. Or that they can simply and easily define range bands specific to that encounter. Maybe you only have Close range in this fight, maybe Medium, and Close…what distance makes sense for a particular range band (6", 10cm, a pen length, "that far")? The important thing is what information is on the map you use, not the scale. Can you determine if a player can get from here to there? Who can they hit? Are there environmental things they can use to advantage or things they need to be warry of? None of that requires a grid. Just a poorly drawn blob on a bit of paper labeled "Sarlacc Pit" with an eraser used to represent the sand skimmer, and a couple push pins to show where C3P0 and Lando fell.
In abstract combat I've seen a map as small as a note card, to one the size of my dining room table. I have used random maps photocopied from old issues of gaming magazines, doodled up maps on some scratch paper, used really cool flip mats, or drawn big complexes on a vinyl mat. For placeholders I've used pins, beads, candy, marker dots, actual bona fide minis, squinkies, a polly pocket, Monopoly pieces, matchbox cars and a chip. All that for the same abstract game.
Or…theater of the mind works too when you forget to bring that lovingly drawn map with you to the game.