I play how I've always played and use Parallel Actions.
I had a chance to sit in with Bob Meyer running his version of Blackmoor and he claimed he ran his game like Arneson. He too used Parallel Actions.
It goes back to the 1 minute combat round idea of OD&D where everyone can do something meaningful in each combat round. You just remove all the granular detail and make it epic. It also makes it so players can do a big combat in about 10 minutes and move back to exploring. It's nice to get in 12 to 15 encounters in a game session.
It is not for everyone though. No minis and pure make beleive requires players who can think more abstractly. I have some programmer types I play with who just can't grasp it fully, they always grumble for using combat grids and figures.