Well, just an update on this. I forgot that I had hyper-v enabled on my system as I was playing around with a VM of Windows 10 before. I disabled that feature and the connected standby started working as it did before.
So now my SP3 "turns off" and on like my phone when I press the power button or when I close the lid. It comes back up immediately like I want it to, without it going into a boot cycle from hibernate.
I left it in standby last night with 81% battery and checked on it in the morning (6 hours) and it had 79% battery left. It came up almost immediately as well, without the boot cycle.