How do you balance writing new papers and revising drafts, especially when working on multiple projects with overlapping deadlines?

My method of setting priorities is simple and hierarchical. 

If a student or a junior colleague depend on the paper, it is the #1 priority.  We work on a 2-week revision cycle, where every key co-authors gets 2 weeks to contribute before passing the draft to the next person. 

If someone pays me as a consultant to work on a paper, that is #2 priority.  In such cases, I do not control the timeline and just do it.  

If no papers meet conditions for #1 or #2, I work on whatever I WANT to write. After all, there is really no point at my stage of seniority to write something that I do not want to. When there is such intrinsic motivation at play to write, then I give that mood a priority and shut off email and refuse all meetings until I have written as much as I want.  Such blocked periods of time can be anywhere from half a day to a week. 

How well has this worked for me? 200+ papers in 30 years and h-index 47. Still want to write a paper or two a year, but will probably end up producing about 4 to 5 papers on average per year for few more decades. 

Writing a scientific paper involves different tasks that require different level of mental energy and creativity. My strategy is to take them at different times of the day, depending on my mental energy level
- Writing things like the Introduction and Discussion, and also the initial planning of the paper, require maximal energy and creativity. I do them when I am fresh in the morning, and save them for later if I feel stuck. That means my energy is petering out.
- Data analysis and making the figures is also high energy, but more mechanical and, in my case, more likely to induce flow. I dedicate to them big chunks of time when I can work uninterrupted.
- Writing Methods and the Results is more boilerplate, although sometimes the Results can be as challenging as the Discussion. I write them later in the day when my creativity is lower.
- Editing is mechanical, although it still requires focused attention. It's something that I do when my creativity and energy are low.
- This allows for strategies to work on different papers the same day. For example, you can write the Discussion of a paper in the morning and edit a paper that is almost finalized in the evening. 
- You need to tailor this to yourself. If you are an evening person and that is when you can write uninterrupted, you may want to write the Discussion and other hard parts of the paper later in the day. 

This depends on work managed by individual or a team.
As an individual writing new task is tedious and ample time is to attributed to this work whwereas draft revision is to allocated relatively <1/4 th of time of writing new task.

The allocation of writing new task complimented with draft time as given time distribution is optimal strategy

I tend to prioritize my own works
However, if deadlines are overlapping, I set precise time schedules 
For instance, I establish to spend 2 hours for my paper and 2 hours for external revisions

Allocate enough time for each based on the deadlines, and act on that schedule.

I follow one simple rule I learned from my old mentor; always prioritise the manuscript closest to being finalised/published. 

This is all about planning and prioritizing work activities. As an academic, your work plan should include an allocated time for research.  This is the time you use for supervision, writing publication, grants and everything else that relates to research. If you stick to the allocated time you will have time to write and revise manuscripts, review manuscripts for journals, etc. The key is that you cannot compromise your allocated research time by using it for other work activities. If you do this, you will loose the plot and start playing catch up or even frustrated and loose control of other work time. Within the allocated research activities, you can prioritise research activities depending on demand. For example, you may choose to finalise a request manuscript revision with a close deadline over writing a new paper or over starting a new lab research. Put simply, it is all about planning, prioritizing and being organised without compromising with other work activities.

I prioritize them based on urgency. Some of them may take over a year as long as we are not pressed by deadlines.

A good researcher must have the ability to read, appreciate other works and have the ability to acquire knowledge.That's the only way you can write good papers. If there is overlapping tasks, a good researcher will find the solution to the problem.

There is no one size fits all. There are different strategies to deal with these challenges. Myself I deal according to priorities provided by deadline to submit or revise. If the deadlines overlap tightly, you can consider the ones that needs more work and ask for an extension.  

#Managing multiple projects with overlapping deadline time is not easy, but a well organized team that works together, by prioritizing the projects and properly sharing the tasks between the agents, arrives in the best of cases to get out of it#

It is always the same! Take them by priority schedule and don't mixt it up.
Then things are going smoothly without problem. You can also delegate part of the work to your colleagues.

I maintain a prioritized task schedule that separates deep-focus blocks for writing new content from revision sessions, align each paper with its deadline and stage such as drafting, revising, submitting, and allocate dedicated weekly slots to revisit older drafts while keeping momentum on new writing—ensuring consistent progress across all projects without burnout.

When working on multiple projects and juggling time and efforts requierd to meet deadlines, I have always  set priorities  based on critical needs of the clients and delgated  certain tasks to my trustworthy staff who could  deliver promised work in a timely manner.

Revising drafts sometimes is more tedious that writing a new paper. I always delegate. My students write the drafts of new manuscripts and I revise the drafts.