You have gotten both incorrect advice and some that is just confusing.

It is very common to change the load by adjusting the input impedance of the phono stage, less common to load the input of the transformer. That's why most phono stages have provisions to change the impedance.

Your transformer doesn't have an input impedance of 250 ohms. That is probably what it gives you when you load it with the standard 47K. Do you know the gain of the stepup?

The impedance is determined by the the input impedance of the phono stage divided by the square of the turns ratio. Just like it transforms the voltage by making it larger, it also transforms the input impedance of the phono stage making it appear to be smaller. So it's not a combination of the 250 and the 47K.

It is very common to change the input impedance of the phono stage to get the load you want on the cartridge. To figure it out you need the turns ratio, or the gain since the ratio can be calculated from it.

You need to choose the right step-up transformer to present the recommended loading of the cartridge AND simultaneously give you the correct amount of gain.

This isn't going to work in real life. Normally you choose the gain you need and then adjust the input impedance of the phono stage to get the loading you want.

The impedance presented to your cartridge will be the combination of the 250 ohms of the step-up and the 47Kohms of your phono stage.

If it did have a 250 ohm resistor at the input of the transformer, the load would be the 250 in parallel with transformed phono stage input impedance, but I doubt this is the case.

I used a K&K Audio step-up with a Hagerman Trumpet. The step-up had a 10:1 ratio. Using 47k ohm resistors in the step-up in parallel with the Trumpets 47k ohms yielded 940 ohms

That math doesn't work. Two 47Ks in parallel is 23.5K which divided by (10 times 10) gives you 235 ohms. To get 940 you would have to put the 47Ks in series.