The Crimson Binome
Hero
There are issues with that approach, where you may end up with details that over-constrain the reality on the ground. If the wizard hits three enemies with their burning hands, and then the sorcerer ends up fireballing the whole group (including the wizard) but misses one of the enemies and hits another enemy that's further away, then it can be hard for someone following along to figure out where anyone really is at any point.You mention AoE spells. I do like how 13th Age does it, where spells and target "Up to two nearby enemies" or "1d4+1 nearby allies". Perhaps a guideline to convert AoEs to that format would be useful.
The basic assumption of 5E is that the only difference between TotM and grid play is whether the DM keeps the picture in their head, or whether they draw it out for everyone to see. The 13th Age seems to be written under the assumption that miniatures cannot be used, because defining such positions would contradict their targeting conventions. Do you know if they have optional rules, to reconcile the two by defining more concrete shapes for their effects?