It might be, but that would require far more work than you probably are prepared to do, and I presume beyond your skillset (no offense - but if it were within your skillset, you would not have to ask probably).
It would not be worth it either way, UCI/LuCI is tied to mac80211 and related modern wireless tools, whatever DD-Wrt uses probably relies on ancient standards and kernels long phased out by now.
4.4 is not supported anymore. At least not upstream by the kernel community. You can check that easily on https://kernel.org/.
An LTS kernel merely implies it gets maintenance (bug fixes, security patches) for a more extended period, but it does not see backports in any meaningful way. So do not kid yourself: you are talking about an old kernel. And an unsupported one, in case of 4.4. 4.9 is the oldest supported LTS kernel at this point.
SLTS is not maintained by kernel.org but by the civil infrastructure project. If you go to the CIP website, they even mention that 4.4 has been deprecated by its maintainer.
dd-wrt is also struggling with Broadcom drivers for being closed source. Their forums advice to buy other brands, unless you refer to older Broadcom, which were supported at the time.
And regarding the OP, I also think it would be a huge effort to attempt a working mix of the two completely different implementations.
It explains some issues on one level and stability on another regardless of the kernel being used but if it is a matter of using a different non broadcom unit I'd prefer to use OpenWRT for it's friendlier forums, documentation.