This Arduino sketch can read and write Nintendo Power SF Memory cartridges without an external clock source like the Adafruit Clock Generator. It also uses the Arduino Serial Monitor instead of the OLED display and buttons.
In the Arduino IDE select the correct Serial Port under Tools then open the Serial Monitor, make sure the baud is set to "9600" and in the box in front of the baudrate there should be "No line ending" selected.
First send "8" via the text box and "Send" button at the top of the Serial Monitor windows. This will switch the cart to "hirom all" mode. It should give you the following feedback somewhere in the text box. Check that it did succeed:
To flash something new you need to erase both the flash and the mapping first before you send the write command. You also need to provide mapping.map and flash.bin files on your own.
In this case rename SHVC-MENU.bin you got from NP Split into menu.sfc and copy it next to the .exe. You can also use a Hex Editor to cut-out the first 512KB of your original flash dump and rename it to menu.sfc instead.
In SF Memory Binary Maker you got two options: either create a standalone map file from a single rom up to 4MB or you can add multiple roms and create a combined .bin and .map file. The sum of all the roms together can't exceed 3.5MB however since you still need 512KB for the menu.
You should end up with a map and bin file, rename both so their filename is very short and without any special characters and copy them to the root of the SD card. Switch the NP cart into HIROM ALL, unlock WP, erase the mapping, erase the flash and then write the mapping and write the flash.