I'm willing to get creative, but I'm out of ideas
Thinking outside the box, computers don't have to go in cases...
If you still want a case and can't find an existing one that fits your needs you could try to make your own. Know anyone with a 3D printer or shop skills?
You don't even need that. A random box will do just fine. You just need enough for the pcie plate to not get in the way. Then maybe something to prop up the GPU so it doesn't tip over depending on how big it is. But I've run a sideways motherboard just fine.
looking at the internal images here..
a 2 wide card looks like it'll fit, if you have the (required) riser card, so long as all the covers are off, and the retention latch is open or removed, and some ''modifications'' (to the chassis back) are made.
but you'll need to secure the card in place, and cover and cool the whole thing..
and then also power it:
the 180w power adapter (laptop style) the builds without a discrete card ships with is most likely inadequate to cover the slot power draw of the 1070, so you'd have to get a larger (and compatible) power adapter. builds with the 50w oem t1000 ship with a 240w one.
and also franken-in a 12v pcie power source for the card, too, as a 1070 can draw at least 150w.