Thanks to the awesome advice from the awesome (baguette-powered) Poudingue, I could dramatically improve the aspect of double blocks. Here is an example with birch doors (I never really enjoyed how they looked, because of the visible seam) and tall ferns.
Please note I also tweaked normals and albedo a bit on the birch door so it looks crispier/more detailed.
For those (I suppose very few) who wouldn't know, Poudingue is the author of Vanilla Normals Renewed pack, which basically is a 16x vanilla pack but with normals and speculars. It retains the whole vanilla experience but adding normals, heightmaps, metallic, roughness, whatnot to the default textures without changing those (apart from removing baked-in AO/shadows).
You'll find his pack here :
for Minecraft ≥ 1.13 : https://github.com/Poudingue/Vanilla-Normals-Renewed
for Minecraft < 1.13 : https://github.com/Poudingue/Vanilla-Normals-Renewed-1.12
Thanks again for you expertise Poudingue, keep up the good work !