I don't know much about movements but I'm fairly certain there is no yuki like equivalent for these type of watches unfortunately bc these need a day function.
I think 2834 and 2836 are basically the same movement so you should be able to use a 2836 which I think would be your best option. They are also relatively easy to find online and not overly expensive.
I would just double check with a modder or watch smith to make sure that it's a direct swap but it should be. I know my day date 40 has one and it's the same case.
I hope this helps
Thanks again! You've got a real wealth of knowledge on this DD40, and it really is quite helpful.
One more question. Do you know if these watches accept any gen movements, or who might know (if you know anyone specific)? Like 3055, 3155, 3156, or 3255?