For the Record  Delivery lead-in
Delivery lead-in   LABORPAINS
Heads-up discovery   LUCKYPENNY [note hyphen]
French bean?   TETE
Chute opener?   PARA   

A fortuitous combination, ARTIE Shaw and Saint-SAENS, as both are musical favorites of mine, and of a million others.  Along with CORNET, they make for a musical northwest quadrant.  BTW, "Eres Tu" is a fine song, especially the way Spanish singer Julio Iglesias recorded it. 
 Make-believe intro
Make-believe intro   LETSPRETEND [also the title of a popular radio show in the Thirties and Forties] 
 Twenty somethings?
Twenty somethings?   ATMS [if the only denomination dispensed were twenty dollar bills]
LIMERICKPOETRY is redundant since we simply refer to it as a limerick.  We don’t say sonnet poetry either as it is subsumed under the class lyric poetry.  Limericks would be under the class of children's poetry or humorous poetry.
60 minuti   ORA [
ora pro nobis is better than the Italian]
Who, in Quebec  CUI [too exotic]
Not under, with “at”   LEAST [an tortured interpretation of the phrase]
Theme: LP phrases seems rather mundane for a Sunday puzzle    
RATING:  Too many problems and a weak theme for my taste.