Rodney, the solo you sang was great. Musical phrasing, interesting ideas, it had a musical arc to it. Bravo. I know your question is more about trumpet but regarding your scatting, I think the only thing you should tighten is the pitch. Getting to the right intonation quicker, especially on held notes.

Regarding trumpet, I can tell that you are hearing a similar melodic quality of phrasing that you can sing. Your 'issue' is the same for all of us: the friction of the horn. As a fellow brass player, I can attest that trumpet of a more difficult instrument to perform the music you obviously have in your head. That said, I think the more your fingers, mouth, and tongue can follow the music in your head, the easier will be the physical playing.

Here's my recommendation for the daily 15 minutes you asked for: 5 minutes of sing a note or phrase, then play that note or phrase on trumpet. Start by playing the note or phrase softly if this is your trumpet warmup for that day. 5 minutes of playing some basic Arbans-style exercises for tonguing and flexibility. Use the metronome (slow to start) as a measurement and discipline for accuracy. 5 minutes of improvising short phrases followed by playing each phrase beginning on new starting notes. Start simple with, for example, the first three notes to "Three Blind Mice". Other phrases could be the first phrase of "Mary Had a Little Lamb", the main motif of Beethoven's Fifth, The first phrase of "Happy Birthday", the first phrase to "Autumn Leaves", or the first phrase of the "Simpsons Theme." Do not calculate the intervals, but instead let your ear guide you. If you make a mistake, resist (again) calculating your way through the phrase. Sing it from the new starting note, then play what you sang, similar to the first 5 minute section of this practice. Expand this 15-minute sequence to 30 whenever time allows.

But listening to the track, I can tell that you have very terrific music inside. Keep on playing!!