As there has not been any further movement on this, I am giving it a go. I have started by re-basing Xiche’s commits on LEDE master (4.9 kernel), then removing some of the bits to build a btrfs image and instead just creating a medkit image as per heinzek’s fork. I haven’t properly reviewed the code so far, but I am able to build a LEDE medkit image that boots on my Omnia. In fact, I am currently accessing this forum via my Omnia running LEDE 
My branch is here: https://github.com/rmounce/lede-source/tree/omnia
I like the approach of only distributing the medkit image, leveraging the Omnia’s built-in recovery to handle btrfs formatting. After a quick look, it should also be possible to update or write another wrapper for sysupgrade so that a single image can be used for both the initial flash from USB and in-place upgrades. btrfs snapshots should also be able to facilitate failsafe mode/factory reset as they do on Turris OS, but this may be a bit more work to adapt on LEDE.
My immediate goal is to distill everything down to a minimal device support patch that I can submit to LEDE for review. Fancier stuff can come later, by that point others should be able to easily install a mostly working LEDE image on their Omnia and help fill in the gaps.
This will be the third time I have seen abandoned yet almost complete patches for a device on my shelf, brought them up on my device, and submitted them to LEDE. They got merged the first two times, so hopefully I can help here.