well, for comparison, those lams are slightly larger than a 1/2", which is what's used in the small API output, the 2623. Those have 3 windings of 75 Ohms each, and are about 600 turns or so. CJ's HS52 sheet above, calls for 2 windings of 255T to make up the secondary (with taps for the other ratios). Anyway, so 500 turns on the HS52 core would give you about 600 Ohm impedance, whereas on the API, it's 75 Ohms. The inductance needed for 75 Ohms is much less, and I'm guessing you'll get just slightly higher inductance on the secondary than a winding of an API2623. So, based on that, pri inductance would be nowhere near what it ought to be, so my guess is it wouldn't work too well.
You can use these for a 600:600 line transformer, sort of like the HS56, although that also uses nickel, it will still work with steel. You could probably build a couple chokes as well, I've seen some about this size. Edcor has some smaller trafos, maybe their site might give you some ideas. For output trafos maybe go with something larger, or nickel or both.