Yeah, I wasn't sure how this would go over. April lies between March and May (both clued). The clue's first incarnation explicitly told the reader to look for a month, but that seemed too obvious -- there's only one month with 5 letters!
With perfect this, you can sing with precision – / Or foster a batter’s “swing indecision”?
1
2
3
4
5
Horizontales
1A
With perfect this, you can sing with precision – / Or foster a batter’s “swing indecision”?
4A
Far from heavy, not quite slight, / At break of dawn, it conquers night.
5A
The soldiers, after a long, long march, had to get ready for come-what-may. / With two words in caps, that’s true for us all! At least we have time, with this in the way…
Verticales
1D
To teach students this, I’d hoist my accordion. They'd all get some beer (me the same). / To guide their dance steps, I’d put dots on the floor, and I’d assign to the dots this apt name.
2D
Stripes of power ‘midst jungle vegetation. / If caught by the tail, a nasty situation!
3D
You had a big day in a strange, distant town, and you are SO ready to slumber! / Go to this place; there’s a room there for you. Let’s just hope you remember the number!