As @
Oofta mentioned
(a) Describe simple rooms or areas with low number of monsters/NPCs and run combat using
Threatre of Mind. It is important you have a table that accepts this style of play - at least for the simpler combats, otherwise you will struggle as I have found out that the younger generation, particularly those heavily influenced via Mercer & Co, dislike this style of format.
I run most online sessions using Theatre of Mind only as I'm not quite there yet with the IT skills on Roll20.
(b) Another method is to loosely draw the room on a piece of white paper, not necessarily in grid format, only enough to assist the imagination of the players.
(c) You can use a grid for the larger more complex combats. I have a player who created two large grid sheets (each A0 size, apologies I don't know if that description exists in the USA) for hexagonal and square grids, and then laminated them. We use markers to easily draw fixtures/fittings (such as pillars, walls, windows, ledges and the like) and tokens for the monsters and PCs. The laminated grid allows for easy cleaning once combat is over - damp tissue works just fine or purchase a sponge. These grids only comes out for combat.
We ran the entire combat of our last session (described upthread) on such grid, colouring in the pillars, holes and furniture.
If you need to end combat prematurely, take a photo of it on your cellphone for next session.
(d) One of the new Mercer-influenced players has tried his hand at DMing and uses Fantasy Grounds with the computer screen turned towards the players. That is also good. You need to find what styles work for the group and do not be afraid to mix it up in a session.
I do very much the same on an excel spreadsheet - which is mostly updated during combat.
Inspiration use, HD, Spells Slots, Hit Points and a few other class/race features/abilities as well as conditions (Disease, Exhaustion and Madness). It is quick and easy like you said.
I tried to keep a log on Obsidian Portal of the sessions but that got away from me pretty quickly - it is too much work and once it is considered work, it isn't fun anymore. These days I only update our Admin Page and Timeline.
I'm thinking of converting our Obsidian Page to a simple wiki for only the most important campaign information i.e. Cult of the Dragon, Ordning, Factions, Council Members...etc