As core size and winding increases you will get a better low frequency but, you will get more leakage which will lose some highs. Transformers do not have impedance on their own. They have reflective impedance, but also power handling capabilities. The impedance is determined by the tubes plate.
The idea is to have a transformer which does not limit, but has the capability to reproduce the Hz needed. For instance, a OT capable of lower Hz will have a larger core and more watts will determine wire size on the bobbin. This will allow for circuit design to determine what the amp will sound like and also push phase shifts below the usable Hz range, but there is a limit and if over-wound you will lose highs.
There are many exceptions and lots of people like to use slightly undersized OT's. The compression of the Princeton is an example when reflected impedance is 8k. Change it to a deluxe OT at 6k6 using 6v6 and it will add more bottom. At least this has been my experience. I am writing this from memory from reading the section on transformers in the
http://www.el34world.com/charts/Books/RDH4.pdfAnd a discussion I have has with HBP. I am sure I have a few things oversimplified, but this is what I remember and also what I have discovered in trying different transformers. There is a simpler explanation I remember reading, I just cannot remember where. A google search may help.
I know this sounds like dancing around your question, but it really is not. I read many pages and experimented. For instance, I have a 50 watt Marshall type amp with EL34's. I put on a OT designed for EL34, but had a small core and had a noticeable increase in highs. Did the same with a OT from a 100 watt el34 and the lower end tightened, but I had to increase the highs some. It is really a balancing act. I just got my hands on a Heybour, 50 watt but have not had the time to check it out.