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Yes, one big difference is there was a lot more warming in Greenland in the MWP than now. Another difference was the MWP lasted off and on for centuries compared to the current single century on and off. Sea levels were the same or higher (up to 1/2 meter higher) then along with other long term warming indicators.

Yep.

Nothing but a distraction from the MWP. There were decades of relative cooling and warming in the MWP. Warm is warm, but you say the drivers are different, meaning evil CO2 is causing warming now but it didn't then. Your cool 1970's memories are matched with skatable ponds in the MWP followed by decades without. The trees are quite irrelevant looking "all sorts of other indicators" available along the ample documentation of historians.

That's a little confusing. I say definitively that during the MWP, atmospheric CO2 concentrations were not changing appreciably, whereas now they are, in the direction expected to increase radiative forcing and contribute to warmer global temperatures. That's a driver now, and wasn't then (ice cores show stable CO2 -- you know that; by the way, have you read Precise climate monitoring using complementary satellite data sets?)

Any variability in the MWP was caused by processes inherent to the climate system then. We do not have any evidence that the proposed primary driver of MWP warmth, ocean current variability, is a factor now --- and ocean current variability operates on longer time-scales than greenhouse gas driven warming, hence the longer MWP time-scales, and also the out-of-phase response in the Southern Hemisphere (Goosse et al. 2003). A lot of MWP discussion overlooks that.

I read the paper, it has interesting data although the authors start with the assumption that the MWP was regional or NH which precludes a more thorough study of worldwide factors (e.g. the Pacific). It obviously helps you eliminate that one driver from modern warming to support your must-be-CO2-SUV theory, but it excludes many other natural driver behind MWP and modern warming so doesn't support CO2.

Did you read the whole paper closely? Check the Mohtadi reference (abstract only, unfortunately) and evaluate it next to the Goosse et al. link. The MWP was warm first in the NH, then in the SH (while the NH was cooling). Multiple lines of evidence support that ocean circulation was the main driver. We do not have a similar situation now.

Yes, CO2 was fairly stable through the MWP, although the ice cores for that period have a right-handed distribution (about a decade or so of substantial smoothing) as the ice sealed. So CO2 wasn't the driver then, no doubt about that. Your painstaking process of elimination doesn't measure all solar influences, natural aerosols, and the longer ocean cycles. The latter is not an either-or like you imply:

We do not have any evidence that the proposed primary driver of MWP warmth, ocean current variability, is a factor now

That is simply wrong, there is ample evidence that the PDO caused the current warming, see fig 3b here:

http://www.drroyspencer.com/research-articles/global-warming-as-a-natural-response/

You can easily cut and paste the usual rebuttal from RealClimate for this paper, but the fact remains that PDO was positive and PDO causes warmer arctic waters and more El Ninos. The worldwide effect can be argued, but warming is obviously in the running.

Alternatively you could argue for ocean acidification or reduced biodiversity and I've always conceded those. But direct climate effects from CO2 pale in comparison to natural variation.