It seems that this issue was due to a mix of two or more settings.
The use of bilinear filtering combined with the scanlines (and perhaps the square pixel aspect ratio) made everything very slow and hard to process for the N2+.
So: everything is back on “auto” except for the shader which is now set on Scanlines, and that is working fine, even with arcade games such as Dolphin Blue (Atomiswave) or the DondonPachi series (Cave) which were heavily struggling when the issue was still present. Now, those games are running great with my favorite shader enabled.
Not really 100% sure about my explanation above, but it was a bad video processing combination, that’s for sure.