Seller insists they sound great and that the primary and secondary imply full spectrum.
That makes zero sense. There’s nothing about “the primary and secondary” that you can tell from outside the can (I assume the seller is talking about nominal impedance) that implies anything about bandwidth. Telephone applications used 600 ohm lines and had tube grids involved, as did intercom systems and other speech applications. So “600:50,000” is worthless as a clue to frequency response.
The only thing that makes me worry is the 300cps-2700cps text.
That tells you all you need to know. 300Hz - 2.7kHz. Speech units.
Caveat: Occasionally, military transformers (indicated by the TF... identifier at the top of the printed text) will have wider bandwidth than specified on the can. The bandwidth the military requires for the application will be printed on the can, per the rules for mil suppliers. As long as the transformer meets or exceeds those specs, it’ll fly. Check any UTC or Chicago catalog, and you’ll see statements to the effect that mil-spec units listed actually exceed their specified bandwidth. But this is by no means the rule. It may be that these fall into that category. But you’re taking a risk. Maybe ask the seller if he/she will take a return if the transformers don’t pass your bandwidth tests.