I had my speaker out at the local swimming hole, and Spotify on.
First Cheap Trick’s “Surrender” played and then “Fox on the Run”. Man those are perfect. They scream 70’s montage at the swimming pool
Others that have that montage feel?
Pretty much anything in Awesome Mix Vol. 1 and Awesome Mix Vol. 2. Both of yours are in Vol. 2.
“Summer” by War should perfectly fit the mood you’re trying to create as should the Isley Brothers’ version of “Summer Breeze”.
I have the clearest snippet of memory hearing Do the Hustle at the local pool in the summer of '75.
In the Summertime - Mungo Jerry
mmm
To go with the two songs the OP listed:
*The Ballroom Blitz *by The Sweet.
“Band On The Run”
Andy Gibb “Love Is Higher Than A Mountain”
Billy Joel
Baker Street
Etc
Summer In The City, by The Lovin Spoonful.
Jungle Love, Steve Miller Band.
“Sunny Days” - Lighthouse
“Do It Again” - Steely Dan
“You, Me and Mexico” - Edward Bear
(if you’re feeling super super wimpy) - “Saturday in the Park”
(wimpier yet) - “Afternoon Delight”
(you have to be kidding me) “It’s a Sunshine Day” - Brady Bunch
(sneakin in a 60’s number) - “Sunny Afternoon” - Kinks
“Smoke On the Water”
“Sail on Sailor” - Beach Boys
Actually can’t think of a 70’s tune that wouldn’t be poolside appropriate. (oh wait - I know - the title track off King Crimson’s Larks’ Tongues in Aspic LP :p) (Alice Cooper’s “I Love the Dead”?:o)
If Eddie can sneak in a 60s number, I can sneak in an 80s number. 
Dire Straits Twistin’ By the Pool.
That reminds me ‘schools out forever’ would be classic material
For those that are wondering what a 70’s neighborhood pool was…
We moved to a brand new housing development in suburban Minnesota in 1970. It had a pool that you could buy a pass to for the summer. It was ludicrously cheap. About 5 years later, because it was so busy, they built another one towards the other side of the development.
Then of course, between vandalism, complaints and the occasional lawsuit, those went the way of the Dodo, being closed down around 1978.
My strongest memory was of waiting outside the gate, being let in and everyone diving in, only to emerge nearly screaming because some idiot poured way too much bleach into it. They had to close it, drain about half the water out of it and refill it to dilute it to acceptable levels.
Long Cool Woman in a Black Dress
Just about anything by Creedence.
Thin Lizzy, “The Boys are Back in Town”
Rod Stewart, “Da Ya Think I’m Sexy?”
Parliament, “Flash Light”
Fleetwood Mac, “Rhiannon”
Oh god no, not “Rhiannon”. That’s not a pool/beach tune IMO.
I’ll add:
“Beach Baby” - First Class
“Get Down Tonight” - KC & The Sunshine Band (actually anything by them)
Anything by The Gap Band
“Hot Child In The City” - Nick Gilder
Ohhh…ETA :
“Jive Talking” and “Nights On Broadway” - The Bee Gees
Aqualung
“We’re an American Band” - Grand Funk Railroad
“China Grove” - The Doobie Brothers
“Saturday Night’s Alright For Fighting” - Elton John
“Son of a Preacher Man” - Dusty Springfield
“Slow Ride” - Foghat
“Sweet Emotion” - Aerosmith
“Thank You” - Sly & The Family Stone
“I Feel The Earth Move” - Carol King
“My Sharona” - The Knack