It turns out that "ARMEX" was a stamp used by a company named Armature Exchange back in the 1930's. They reference rewinding armatures "made 15 years ago" which would put it squarely in the "T" era. And I have a couple.
I found the text of a lawsuit they filed against the government (IRS) arguing they shouldn't have to pay excise taxes on sales because they were not the "manufacturer", only a service provider.
The lawsuit is circa 1939, for work done in 1933-1936. The most interesting part is the VERY lengthy and detailed description of how one goes about rewinding armatures.
And this tidbit:
"The rebuilt armatures are sold, in most instances, to jobbers who bring in old armatures in exchange — the plaintiff's charge being merely for the rewinding, and ranging from $2.50 to $22.50. If a sale is made to one who does not bring in an old armature, an added small charge of from fifty cents to a dollar is made for the core."
If ONLY I could get an armature rewound these days or $2.50! Today it's more like $200....
If only I could also get cores for $0.50 - $1.00 from Glen Chaffin

https://casetext.com/case/armature-exch ... ted-states
judgement was originally in favor of Armex, but reversed in 1941 in favor of the IRS. 2 things are certain in life..... Death and Taxes.
https://casetext.com/case/united-states ... e-exchange