Solar variation is not the cause of the current warming. Got that? Good.
It's not "the" cause, but it is a cause of current warming. It appears to me that we would be among the hottest temperatures for this interglacial period even in the absence of human contribution to global warming.
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.
We don't have similar past measurements of solar activity, so we don't actually know the degree of contribution from solar activity to the current degree of warming.
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."
Or that there was a lot more radiative forcing than expected. In addition, the Maunder minimum happened just prior to the start of the industrial age. The current claimed degree of human-generated warming is based on an assumption of very little increase in solar output from then to now. If the solar output increase is much greater than claimed, then the human-generated contribution has to be smaller as a result.
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.
I see considerable evidence out there, such as the factor of three difference between lowest and highest estimate of the radiative forcing of CO2, to indicate that we don't understand climate well enough. And if we "don't know", then why is there a "best understanding" that conveniently dismissable volcanic activity was responsible for the Little Ice Age? There are a lot of assumptions that all go a politically and ideologically convenient direction.