I believe one of them was already started before poll results and the other one started after. Both took around 1 year.
Skarner actually didn't take too much more than that. However, we announced the poll before we were ready to start because Udyr was heavily delayed.
Udyr was heavily delayed because he was generally a very very resource heavy project. His various forms and ultimate skin took a long time especially during a global pandemic. TBH, during the pandemic, while I was not on champs, there were days where I was just heavily depressed and just wanted to sleep all day...
We also went through a period where we are training new designers, animators, VFX etc etc up on the team. This is good for overall health of League. It was how we are able to staff up modes. However, first projects are always a painful one for team to figure out how to work together.
Being honest, Udyr was not easy because of the bulk and Skarner started turbulent. We did not really dive deep into Skarner till Udyr shipped. Especially because Skarner's story is very intertwined in Runeterra and we were working with changing narrative landscape at the start.
All in all, each rework takes around a year + based on complexity of skin and experience of the pod. This make polls very not fun to run as a dev. Mostly because the ones that lose, feels bad. The ones that win also feels bad to wait around 1+ year.
The good news, is that I very much understand the want as a player to have a voice and a choice. I will noodle on the ways to make this more satisfying. Moreover, our team can only grow and become better at what they do from here! We are working on strategies to support the overall health and sustainability of League. Personally, I don't want League to look like a 20 years old game in 5 years! I want us to still be the shiniest on the block :D