… do they have a name? By phonetic anagrams I mean phrases with identical sounds except for a phoneme displacement rather than a letter displacement. I just stumbled on one I rather like—
dinasaur shoes
Dinah Shore sues
More importantly, do you have any good ones?
Do you mean something like: Lebanese lesbian?
djm
No, you get from one of my phrases to the other by swapping ‘s’ and ‘sh’ phonemes. In an ordinary anagram you get from one phrase or word to the other by a letter displacement as in ‘rattles’ and ‘startle.’
Hey, wait a minute. You’re at the very least close; in fact I think you have one.
Okay, how about, “Not now, Pous,” which is “won ton soup” backwards?
djm
Hmmm…I’m going to have to think about that phoneme displacement requirement. So far the only thing coming to mind is the old church hymn about Gladly the Cross-eyed bear.
Different game.
On third thoughts, your first example isn’t quite there. Close, but no cigar.
So basically you mean a Spoonerism, but more rigorous, right?
I thought of ‘I saw Iraq and Iran’.
That’s not what you’re talking about, but it was a good decision on my part. 
Here’s a famous one that’s close without quite getting there:
I’d rather have a free bottle in front of me than a pre-frontal lobotomy.
You can knock me down, but you can’t knock me up.
djm
She sells seashells…?
Or how about, the difference between a girls’ track team and a bunch of clever pygmies: the one is a bunch of cunning runts.
Or how about, the difference between a woman in the bathtub and a woman in the Salvation Army: the one has hope in her soul.
djm
Aha, like what tompipes used to have as his siggy: “I’m a pheasant plucker…”
That’s right. Good examples are tongue-twister fodder.
Whoa, deej! This is a family show! 
Dirty, dirty, dirty.
Who’s a dirty bird?
djm
I’m coming up with punchlines to old jokes.
Like Rudy the Bolshevik whose wife skeptically questions his weather-predicting ability, to which he replies “Rudolph the Red knows rain, dear.”
Or the bartender who has to confess (to the doctor who always comes in after a hard day to unwind with an acorn daquiri,) that he’d run out of acorns and had to substitute hickory nuts. “You’re right…it’s a hickory daquiri Doc.”
Oh, jeez. How about that one where a fellow suffering from irregularity consults a Chinese herbalist, and the punchline is, “With fronds like these, who needs enemas?”
The hairs on the back of your neck should be rising right about now…
The version of Wombat’s that I know is:
Better a full bottle in front of me than a full-frontal lobotomy.
I used to know a bloke that thought it was enormously funny, but he could never say it. In fact he never managed to say it properly in all the time I knew him. That was funny.
Here’s one I wowed them with a week or two back:
Fashionable River-craft
Mrs Puggy-Wuggy has a square-cut punt
Not a punt cut-square
but a square-cut punt
It’s round at the end and blunt in the front
Mrs Puggy-Wuggy has a square-cut punt.