A 0.67mm hole was for a 0.55mm soldered round pin (it is round, right? Because a square is too large and won't fit) is actually higher precision than a normal soldered hole so I don't see foresee any problems there as long as you can overcome the heatsinking of the board to solder.
Use a giant tip. Even if the tip is larger than the pad if there are no surrounding components to prevent you from squeezing it in. I think you can do it as long as you can squeeze the iron in.
I've soldered 4-layer boards with 2oz copper on the outside layers using leaded solder without much issue as long as I could fit a large tip in. The only ones that gave me issue were tiny surface mount pads without thermal relief that connected directly to a plane and those required a preheater.
For those it turned out a flat faced bevel tip with tinning only on the face and not the sides really helped because it holds a solder blob right on the tip that that can squeeze into the nooks and crannies and make real good contact on the smallest pads. The blob pulls away with the tip so it behaves like a liquid metal tip.
But I never found through-holes to be an issue at all.