It occurs to me maybe you're being too specific about the meaning of another heartbeat soothing a puppy and a baby.
The two 'examples' in the two Stanzas simply explain the concept.
The Chorus turns philosophical, generic, the narrator taking over and
As always I want to see the 'furniture' of a Singer-Character and a Love-Interest-Character and the simpler concept of hearts in love.

The timing of another heartbeat is a concept. "I wanna get to you, Before Another Heartbeat."
"I wanna tell you now, Before Another Heartbeat."
"I wanna talk to you, Before Another Heartbeat."
"I need to get to you..."
"I need to kiss you now..."
"I gotta..."
"Com'ere Baby! Come and let me feel, Another Heartbeat."
"I just need to feel, Another Heartbeat."
"Com'ere Baby!
Don't waste Another Heartbeat."

I don't think you can space Another... Heart... Beat... and get the Rhythmic effect of the natural speech of how you'd actually say it.
Puh-dum-a dum-pum!

There will always be another song to be written. Someone will write it. Why not you? www.garyeandrews.com