Yes, 10 to 20 seconds is where I'd put it, though I also agree for the need for some scaling. Actually, the problems with 5-6 seconds and also with 1 minute are that they are too far to the extremes of the practical ranges, making the scaling more difficult. If the default is somewhere around 10-15 seconds, then it becomes easier to have modules scale for shorter or longer without so many side effects.
The 1 minute round is really meant fo dungeon exploration and/or or wilderness skirmishing. It can make sense in that environment, because it's assumed that a great deal of time is spent skulking and moving. For example, "The Howling Tower", a Fafhrd and Gray Mouser early adventure as a scene where they fight some bandits while circling around the woods of a clearing, with said tower in the middle. No one wants to go out in the clearing and give away their position, but no one wants to leave the edge where they can't see the clearing. Everyone in the fight knows this. So you have pauses in the action until two opponents close, whereupon it ends rather quickly.
Of course, you could also do a hybrid approach that had distinct "skirmish" rounds of longer duration, but then close melee rounds with limited options happening far quicker. Average spell casting to mainly work in the skirmish scale, which puts a caster at a disadvantage in melee (absent certain key spells designed just for that). Something like this might do a better job of handling the pacing (stalking, building action, followed by relatively rapid resolution) than a set scale, and would also enjoy the best of both worlds for ease of play.
Perhaps it would help if we didn't call the 1 minute duration a round. If it best serves for tracking time and events at the exploration level, it would seem best to focus on that as a mechanic. For now, I'll call it a
Segment.
Segments
A segment is a set period of time used for tracking player actions when time might matter but you don't need to detail of combat rounds. As DM, you choose how long a segment is (1 minutes, 10 minutes, an hour, etc.) based on the scale needed. In a dungeon with active inhabitants, you might want a one minute segment. When tracking actions in a city, you might choose a one hour segment.
During each segment, ask the players what their characters do. If there are monsters or other active elements in the vicinity, determine what they do as well. You may want to keep track of this.
PCs may take whatever actions are reasonable during a segment, and you may determine how long certain actions take. For example, if you're using one minute segments, and a PC wants to search a large room for secret doors, you may determine that doing so will take 3 segments.
Combat During Segments
When combat happens, players roll initiative and you start tracking rounds. When combat is finished, you return to tracking in segments. For tracking purposes while using one minute segments, it's usually best to assume that a short combat takes one full segment.
Sometimes, you may not need to roll initiative for combat, though. A fighter holding a barricade, or a wizard casting a spell at a group of goblins that are out of melee range might best be handled using segments. These are cases that are more story driven than tactical in nature. Use your best judgement. If a situation becomes more complicated, you can always roll initiative.
With something like this, segments are more of a tool than a mechanic, while still giving you something to hook mechanics onto. For example, random encounters or events might be rolled for each segment. Nothing here is new, but it does provide a name for a unifying concept.