I think you are pushing your own idea into the text.
...5 The waters continued to recede until the tenth month, and on the first day of the tenth month the tops of the mountains became visible.
... 9 But the dove could find nowhere to perch because there was water over all the surface of the earth....
It is very clear to me that the mountain tops were still submerged but you could see the tops just under the water if you looked over the side of the boat.
Its even stated in 9 again that the water covered everything.
“Seems a careful reading forces one to take “over all the surface of the earth” to at least not include the mountain tops in verse 5.” - You project that the MTs are sticking out of the water.
- Seems to me a MORE CAREFUL, CAREFUL reading should be done. - I have see plenty of submerged Rocks, Islands, while in my boat... I even hit a few too.
Mountains as we all know tend to vary in height both in the parts of the mountains and different mountains. Water on the other hand tends to be much more uniform and is pretty much the same height excepting for tidal forces and waves in a given broad area.
It seems reasonably likely for them to sail close enough to the tallest mountain top in the area that happened to be close to the surface that they could see the peak.
It seems less reasonable to expect they sailed close to several that were close but none of them breaking surface.
And it seems not even plausible that they sailed over the highest peaks in the world, namely Mt Everest way to the East on the border of Nepal or Mauna Kea in Hawaii.
So upon reflection this interpretation seems to have problems being sensible.
The only way to save this interpretation it seems to me is to suppose Noah (or the author of this part of Genesis) was given a special revelation from God that the highest mountains in the world were indeed visible even though Noah and the ark was nowhere near them so Noah would not be able to see them himself.
Looking up The Masoretic Hebrew for Gen 8:5 I see that the word for visible is רָאָה which is Strong's h7200. English translations either use "became visible" (such as NIV) or "was seen" (such as ESV). The Strong's definition for the word suggest to me that they meant was visible such that it could be seen (disclaimer I am no Hebrew scholar, although there is one at my church I think I will ask when I get the chance).
Link to Strong's for this word
I am afraid it seems very much more reasonable to interpret that Noah could see some mountains. And even if this meant the ones he saw were still underwater certainly taller mountains in other parts of the world were not.