"...the depth of x, y, and z that currently overwhelm(s?) me."

Solution 1:

You're right about what the question boils down to (whether it's the "depth" or the list of nouns doing the overwhelming), but it is "depth" and therefore "overwhelms".

Cutting out all the extra-informational bits of the sentences leaves

"The depth ____ [overwhelm/overwhelms] me."

In that form, we can see that it's similar to saying

"The bundle of sticks ___ [is/are] lying in front of the fireplace".

We see that it should be "is", because the subject of the sentence is "bundle" and "of sticks" is just modifying the subject.

With your sentence, "depth" is the subject"; "love", etc. is just giving us more information and is not the subject. Therefore, the verb should apply to "depth".