I listened to a few of the other versions I have (the versions I have with words, not the instrumental versions), and I kept finding other interesting things about the song.
The next version I listened to was by Charlie & His Orchestra. It's from a set of World War II-era music, specifically the CD of the German propaganda pieces. It's also the first version of "Dinah" that I ever heard. In their version, they actually emphasize that "Dinah might"/"dynamite" feature. After going through the verses normally, there's the propaganda section, which mentions Churchill's fear of naval attacks: "Every night / Why does he / Shake with fright / Because some dynamite / Might sink us all in a day" (the Germans were singing as if they were the British, hence that "us"). It was fascinating to see that Germans in the 1940s noticed - and made use of - the same sonic feature that I did.
After that, I listened to Bing Crosby's version (which I later learned also features the Mills Brothers). While listening to his version, I noticed that there's a line break during the word "into." Instead of "How I love to sit and gaze into the eyes of Dinah Lee," it's "How I love to sit and gaze in / To the eyes of Dinah Lee." Later I realized that the line break's occurring within a word indicates how enchanting her eyes are: it's as if the speaker/singer can't pay attention to the structure anymore.
Listening to Crosby's version also got me thinking about "my Dinah might / Change her mind about me." The "Dinah might"/"dynamite" suggests that Dinah's "chang[ing] her mind" would be as devastating to the speaker/singer as a literal explosion.
Yester-day, I learned (I think correctly) the chords to Crosby's version. During that bridge, there are descending chromatic phrases within the chords. It's D minor, F augmented, F major, in which is the chromatic phrase D, C#, C. Then there's D minor, F augmented, C major, with the same chromatic phrase. Traditionally, descending chromatic lines are indicative of despair, and that's the case here too, since the bridge is the only section that's sad or fearful. The verses are about Dinah's peerlessness:
Dinah, is there anyone finerher enchanting beauty:
In the state of Carolina
If there is and you know her, show her to me
Dinah, got those Dixie eyes blazin’and the speaker/singer's dedication to her:
How I love to sit and gaze in
To the eyes of Dinah Lee
Oh, Dinah, should you wander to China
I would hop an ocean liner
Just to be with Dinah Lee