The biggest problem with the instrumental period is it is too short. BEST has currently the longest instrumental record and that has issues with other influences than just Solar Volcanoes and Carbon Dioxide. Scaling BEST to the Hadley Center Sea surface temperatures adds a lot of confusion, but it helps complete a bridge to paleo reconstructions, provided you remember the uncertainties.
With this chart, Sol yVol likely started the Little Ice Age around 1240 AD. It took about 500 years for the IPWP to cool to its minimum and so far it has taken about 300 years for the IPWP to recover. Remember that BEST is scaled by 0.55 to make this splice meaning that warming of the land areas would be about twice the warming of the IPWP. At the 1955 end of the Oppo reconstruction, it was still showing a weakly damped oscillation with a period of roughly 62 years. That is the same rough period as the Atlantic Multidecadal Oscillation (AMO) which is about twice the period of the Pacific Decadal Oscillation (PDO). In the southern hemisphere the ~62 year oscillation is muted by the more efficient mixing and can be interpreted as a centennial scale oscillation in the Pacific which if you consider a mix of 62 and 31 year recurrent recovery oscillation would appear to be a 93 year oscillation. You can pick nearly any period that is a multiple of above or below ~31.5 year base frequency you like, if you are in to being a cyclomania.
Is this fit convincing? That depend on on how faithful you are to your personal theories. Given the magnitude of change is roughly +/- 0.5C degrees "Globally" in a thousand years, I doubt it much matters.