Would it be correct to merge with hyphens one-third-contiguously in the following phrase?
No. "One-third-contiguously" would indicate things that are only partially contiguous, which means that they would abut at something less substantial than a mathematical point (the minimum requirement for contiguity), and the whole phrase being used adverbially. Perhaps if you were to put it into context someone could suggest a wording less damaging to Broca's area.
If you want to modify "one-third" with an adverb, put it in front with no hyphen:
However this tends to modify the amount, or how confident one is about the precision; I'm not sure exactly what you're saying but using "contiguously" in this position would sound strange and the meaning would be unclear.
You may better off using an adjective instead:
but inserting this back into your original sentence makes it clumsy; depending on your precise meaning something like
may be your best bet.