There's a way, but only if you're on PC.
1. download and install the overlay on-screen ruler (I used MBRuler in 'coordinate grid' mode),
2. go to the Mirror in Black Emporium with your character
3. use the overlay screen ruler to get the exact grid coordinates for your features and write them down.
4. start your new game and put all the grid sliders on their proper spots.
It's important to keep DAI in 'windowed fullscreen' all the time during the process, and to keep the '0;0' ruler starting point at the same place (it remembers the position unless you move it around manually).
It's also easier (at least for me) to control the CC with a gamepad, while operating the ruler cursor with my mouse.
The non-grid sliders (like eyes shape or hair color) are easier to get - just count the 'clicks' you need to make from your position to the 'zero' option.
It took me something like ~30 mins total to recreate my custom Inq, measuring the 'face-code' and making a new one in the CC. I've also measured the 'face-code' for another custom face I'm going to need later on during my PT, and by that moment I would only need to turn my magic ruler on, no more hours of painful trial-error.
The only option for the console players are the duct tape and\or a regular ruler (or a measuring tape), unfortunately. Sounds brutal, I know, but is going to work nevertheless.
You just need to get those bloody numbers somehow.
Or you can load your earliest post-intro save and start from that point as if nothing had happened yet. But that's if you have that early save.