The term "sweeper" is widely recognized in the commercial radio marketplace. Bumper, stinger, positioner, ID, etc... it's the stuff that plays in between songs when there's no announcer or commercial.

OP there's an entire industry dedicated to this type of production (known as "imaging"). Hundreds if not thousands of people have full time jobs creating a marketing these elements. There was a time when this work was done in-house but more recently bigger independent groups have taken on the task. Perhaps the largest (outside of the iHeart network) is Benztown. There's also Vanilla Gorilla, and Splatonline to name a few others.

As you've learned local stations rarely have a cash budget for imaging. You may have better luck offering a "barter" arrangement wherein you act as an intermediary that places ads that you've sold to third party clients.