Origin of the phrase "dotting the i's and crossing the t's"

I believe your explanation is the logical one, although I don't think most of us ancients who were taught cursive were told to wait until the end of a sentence to dot and cross.

dot the i’s and cross the t’s

Be meticulous and precise, fill in all the particulars, as in Laura had dotted all the i’s and crossed the t’s, so she wondered what she’d done wrong. This expression presumably began as an admonition to school children to write carefully and is sometimes shortened. William Make peace Thackeray had it in a magazine article (Scribner’s Magazine, 1849): "I have...dotted the i's." AHD

Where did this expression originate from? The expression actually came from the writing world. Some writers have the habit of writing a complete sentence or phrase containing several i’s and t’s without dotting the i’s and t’s until they finish the sentence and put a full stop before they go back and dot their i’s and cross their t’s.

Now, in the course of doing this, some writers tend to forget to dot some i’s and cross some t’s in their sentences. This therefore means that these writers did not pay close attention to the details.

It is from this that the expression ‘dot your/the i’s and cross your/the t’s’ came from. hosbeg.com

If you say that someone dots the i's and crosses the t's, you mean that they pay great attention to every small detail in a task; often used to express your annoyance because such detailed work seems unnecessary and takes a very long time. Collins