Good find! Here's the lyrics printed from the above link. Unfortunately, it doesn't appear to be the same as the lyrics from Songs of War and History. They're substantively similar to the Sons of the Pioneers rendition above by wysiwyg. Unfortunately the article did not specify if Stone was their source.

Normally papers would only print snippets of songs, but this is long enough to be the whole thing. The only way I can find to check as of now is if someone has access to The British Library in St. Pancras.

As for the status of the name being a pseudonym, the catalog entry normally indicates if it's under a pseudonym or not. The copyright catalog lists the name as CLAIR M. STONE in one place and Manny STONE in another.

Aside from separating by stanzas, this is as printed in The Grand Prairie Texan, August 30th 1935. All typos are as printed in the original.

WHEN OUR OLD AGE PENSION COMES TO OUR DOOR

When our old age pension check comes to our door,
We won't have to skimp and worry any more.
Every dog can have a bone,
every kid an ice cream cone,
When our old age pension check comes to our door,

When our old age pension check comes to our door,
We won't have to eat hamburgers any more,
There'll be liver for the cat,
now she's lean but she'll be fat
When our old age pension check comes to the door.

Sell your troubles for a song and learn to sing,
The word depression soon won't mean a thing.
Times are surelly getting better day by day.
When our old age pension check arrives we'll be okay!

When our old age pension check come to our door,
Every kid will love his Grandma even more;
Mother-in-laws who are old,
won't locked out in the cold
When our old age pension check comes to our door,

When our old age pension check comes to our door,
There'll be jobs and opportunities galore;
We'll buy classy clothes and cars,
we'll buy planes and fly to mars,
When our old age pensions checks comes to our door.

When our old age pension checks comes to our door,
We won't see old man depression any more.
Like a dog that's had his day,
we'll just pension him away.
When our old age pension check come to our door.

Take a dose of laughing gas and learn to smile,
after whille,
We'll be rolling in the clover after while,
Thank the Lord we're growing older day by day,
When our pension checks arrive we'll be okay!

When our old are pension check comes to our door.
Every man will love his neighbor as of your,
We'll all learn the Golden Rule,
ride to glory on a mule,
When our old age pension cheek comes to our door.