Does Tiruvaradhanam fall under Nitya Kainkaryam (daily service/duty) after performing Sharanagati? Due to a lack of time, I only do Nivedanam (offering of food), Japam (chanting), and Parayanam (recitation) daily. I perform Tiruvaradhanam only on important days.

Whether it is before or after Sharanagati, Tiruvaradhanam is a Kainkaryam (service) that must be performed daily. That is why the Smritis and Agamas state that Tiruvaradhanam is a Nitya Kainkaryam (a mandatory daily duty). Therefore, it is good to perform Tiruvaradhanam daily to the extent possible.
If you are unable to do it, you can have the elders or youngsters in your home, such as your son and others, perform it.