Singular or plural verb form where subject includes a "parenthetical" element
Solution 1:
The question seems to me to turn on whether or not as well as is a coordinator. If it is, then the following verb behaves as if and had been used instead, that is, the subject becomes plural and so does the verb. But as well as says something that and does not. And places the two items on an equal footing, but as well as gives grammatical priority to the first item. How would it be if the sentence were The title in addition to the tone of this volume err(s), perhaps, in being unduly modest? That means much the same, but if you have reservations about making the verb singular after as well as, you may well have far fewer reservations about making it singular after in addition to.
Solution 2:
My inclinations are the same as the OP's (err in the first sentence, errs in the second). But according to The Cambridge Grammar of the English Language (p.1316) our inclination in the first case would be wrong. It cites the example:
- Beauty as well as love is redemptive.
and explains the singular verb as follows:
" ... the 3rd person singular verb-form is indicates that the subject is singular: is agrees with beauty, so that as well as love is treated syntactically as an adjunct, not as a coordinate."
Addendum: the passive phrase "is treated syntactically as an adjunct ... " in the reference book's explanation does not specify the agent. In this case I interpret the agent as akin to "English grammar". An alternative interpretation is that the agent is the speaker of this specific sentence and he or she is treating "as well as love" as an adjunct not as a coordinator. Hence the singular verb.
Elsewhere in the Cambridge Grammar are references to what are termed "singular / plural overrides" where the speaker indicates his or her interpretation of the subject as being singular or plural, irrespective of its grammatical status. Something similar may be going on in the OP's quoted sentences. Writer 1 is interpreting tone parenthetically and writer 2 as a coordinate of title, hence their choice of verb number. The problem is that their punctuation, or lack of it, may confound readers' expectations.