But the solar variation is not ten times as much. We measure the solar output. We know that this is not responsible for the current warming because we measure it.
Nobody measured solar output during the Maunder minimum.
You are confusing two different things.
Solar variation is not the cause of the current warming. Got that? Good.
The climate in 1700 is somewhat harder to model. You quoted what I already said, and I see no reason not to just repeat it:
Well, except nobody knowns whether the Maunder minimum even had anything to do with the little ice age, except for the coincidence of timing. The best understanding at the moment is that the little ice age was due to volcanic eruptions:
That seems straightforward. Nobody knows if there's a connection.
Your comment on that post is
We see here a willingness by researchers to rule out conflating factors despite having insufficient evidence. That is IMHO evidence for the bias I referred to.
I don't understand your logic here. Those "conflating factors" in analyzing climate of the 14-19 centuries don't have anything to do with current climate. For that we have measurements of solar activity.
People have been looking for a solar activity/climate connection for literally hundreds of years*. They haven't found it yet. Understanding the connection between the Maunder minimum and the little ice age, if one exists, would be a huge advance in climate science. But it's not really possible to do science on the basis of "here's something we don't know because the data is poor or non-existent. Maybe there is something we don't understand, but we don't even know if there's anything there."
However, here is something to think about. If it were discovered that the solar variation during the Maunder minimum caused the temperature drop of the Little Ice Age, that would make the climate scientists say "oh my god, the highest estimates of warming due to the greenhouse effect are the right ones; it's a lot worse that the conservative estimates."
Because if the Maunder minimum actually did cause the little ice age, that implies that there must be a big positive feedback loop between radiative forcing and climate. The exact size of the feedback look is the main uncertainty in climate. The short term feedbacks are getting to be well understood. But if there's a large long-term feedback-- one that hasn't really kicked in yet-- then the greenhouse effect is really much worse than the average of current estimates.
But, in either case, whether the Maunder minimum does or doesn't explain all or part of the little ice age isn't really relevant to the question of whether we understand current climate, because we don't need proxies for solar activity to understand current climate: we have measurements. Saying "we haven't found a connection between the Maunder minimum and the climate" isn't bias-- it's just a statement of what we don't know.
*mostly in the century-long series of studies trying to understand the cause of ice-age cycles.