Sounds almost right. I am familiar with the Petersen Device. Designed by John Petersen (not 'Peterson') the same man who designed the (original) Model 51 .32 ACP Remington pistol of long ago.
There are three serious problems with the idea.
One, the device was destroyed en masse by the Army except for a few kept for the Ordnance department (Museum, probably). According to all the literature, there are very few left and and are rather spendy collector's items. No one makes replicas devices to my knowledge. Advertised on one auction website, expecting $25 to $30 THOUSAND for the winning price.
Two, presuming one obtains a Petersen Device, it only works on M1903 Springfield rifles that have been modified to fit the device. Among possibly other things, an ejection slot in the left side of the receiver. I do not have such a rifle, and they are collector's items and cost more than a pristine M1903 Springfield and that's more than I want to spend.
Three, the Petersen Device was NOT chambered for .32 ACP. It was chambered referred to by the U. S. Army as "Cal .30 Auto, Pistol Ball Cartridges, Model of 1918". Labelling them as 'Pistol' cartridges was primarily to conceal the true of the ammunition from the enemy to my knowledge. The design and shape of the cartridge looked like a pistol round, much like the later .30 M1 Carbine round. It was not the same as the .30 M1 Carbine round, either.
The round was designed specially for this use only. According to some stories, it was later used by the French as the prototype for the French .32 long pistol round for the French pistol 1935A and a submachinegun and so on.
The ammo used to be available as surplus. I found some ads on the internet, about $30.00 plus shipping for 50 rounds.
So the idea is not cheaper than reloading for a rifle. Not a bad thought except for that.