What is the verbatim (grammatical) meaning of 不了​了之?
Your understanding for 不了 and 了之, respectively, are accurate. The key to your question is the relationship between the two parts. 

In classical Chinese, omission of conjunctions is a very common thing, which brings beauty and ambiguity at the same time. In most cases it's intentionally left blank for the reader to interpret. There is no single correct answer. Even with the presence of a conjunction (e.g. 而), it could be just a syntactical tool without nailing down the logical relationship between two clauses. I believe this is the case in 不了了之. The most natural conjunction, if to insert, is 而 i.e. 不了而了之, however it is still unclear whether that's an 'and' or a 'but' or anything else. 

One thing clear though is it's definitely not a strong causation (e.g. 'if-then'). But it could really be anything depending on the context from weak causation, adverseness/comparison, concession to simple time continuation. Some possible translations:


Ending without finishing. 
There is no resolution but it's ended. 
Settle by leaving unsettled. 
Although it's not resolved, leave it be.