[Samsung Galaxy J7 Questions & Answers] Droidriven:
I know what you're talking about, you can get to download mode from there, I had to figure out myself. I'm not sure exactly which part of this is what made it work, but, what I did was:

1) With the device powered off, connect the device to PC with Odin open on the desktop, let the charging animation do its thing until it reappears showing how much charge it has.

2) boot into the unknown power reset screen, with the device still connected to PC(with Odin open), then press and hold volume down+power for 7 seconds as it describes on the power reset screen

3) when the 7 seconds pass and it triggers the reboot(timing is critical on this next step) as soon as the screen goes black, immediately release the power button and immediately press and hold the home button but continue to hold volume down without letting go. You will press and hold the volume down button the whole time in the process, you just need to switch your fingers immediately from releasing power button to immediately pressing and holding the home button at the very moment the screen blacks out to reboot, while connected to PC.

Did that make sense? If you get it, you will boot into download mode as soon as you press the home button after releasing the power button.

Then you can flash the stock firmware. I had to do this when I got home today. I flashed the engineering firmware, when I went to flash one of the other stock firmware I have, I kept getting binary errors. I had to download BSJ1 overnight and flash it today after work. Keep trying what I said, try different ways and sequences of actions, that is what I did to discover how to get into download mode from the power reset screen.

By the way, the engineering firmware has an app that can be selected to reboot download mode directly from system, but it requires a password or code that I don't know.

I have a USB jig, but it didn't work. But, I bought it years ago. It works on devices that are triggered by 300k resistance(older devices), most newer Samsung devices are triggered by 301k resistance. You would specifically need a USBjig with 301k resistance. But, I'm sure you can get the trick I described to work, just keep trying, I know for a fact by first hand experience it can be done. I've gotten it to boot to download mode several times after triggering the power reset screen. I kept trying to reproduce the effect, in an effort to identify exactly what I did to trigger it correctly into download mode. What I described is how I got it to consistently boot into download mode then power off, reboot to power reset, reboot to download mode. Once I cycled through a few times, it got easier.

****Side note****

I completely forgot that I have a J737A sitting in a drawer. I found the engineering firmware for it also. I don't plan on using the device, so I'll go ahead and use this for testing. If I get something to work, the method I use should be applicable to all of J7 variants, it would just require some things to be specific to the device in question. One thing I noticed though, the 737A has 7870 CPU and we have 7885 CPU, yet our device is supposed to be a rebranded 737 variant.