I also think the trick to getting everything done correctly and on time is to manage your time in the most orderly manner possible! I don’t know how much time you have on your hands but a good idea is to structure your day in hour slots! For example 9am-10am/check emails , 10am-11am/reply emails , etc etc etc
Obviously it will change from day to day but at least have a structured schedule so you will not get distracted from what you need to do! Also use post it notes to remember important things!
But basically that’s how I work on a daily basis, structuring my day by hours so I don’t get off track!