Any tricks to winding high ratio, high impedance RF transformers

Let's start with, there is no need for an amp with a 260ft antenna in the AM band. I have a fet amp, it has a gain of 1. It has a high input impedance and low output impedance.(power gain) It has some gain 6 or 8db over using a matching transformer. I wanted to see if I could get more gain, that would be by using a step up transformer on the input of the amp. Thus the 350 to 23k transformer. OK, that didn't work. I have a couple Norton noiseless feedback amps if I wanted to use them, I don't. I did figure out a way to build a 350 ohm to about 20k, I might be able to get it to 24k, just haven't tested it. It's not practical, but it's doable. It uses 2 turns and 14 turns on one core, and do that on 10 cores. Then connect primaries in series and the secondaries in series. I got as far as two cores and the numbers were good. Lost interest, I got my antenna working. The amp works, doesn't improve anything, but the system works. S meter jumps 2 to 3 units when I turn the amp on. I got a new toy a Nano VNA H4, I want to start learning to use that. Mikek