TLDR
Not in any user friendly manner that fits in the limited time budget a mod like this written in my personal free time has. I think I have an approach, but I still have to think it through.
Long version
The centering point issue is as old as this mod itself. I started with 0,0 to get a quicker "minimal viable product" out, but dropped the idea to change it.
My first approach was to always center the image perfectly on the base (aligned on chunk corners) so the resolution would always be utilized perfectly. This would have the downside of timelapses "jumping" all over the place as the center would move very often, rendering the timelapses unusable.
My second approach was to center the screenshots automatically on the position of the first entity you place. This was dropped as this would result on basically the same images as 0,0 on a default nauvis run with no other surfaces. At that time I didn't even really understand how surfaces worked.
My third approach was to somehow get a centroid or average position of every block on a surface to center the screenshots kinda automatically on the center of the base. But when expanding straight upwards this would still result in almost empty images. Also, this would be very expensive to calculate compared to the very simple calculations I currently do everytime the player builds or the ones I do everytime screenshots are initiated.
My fourth approach was pretty much your suggestion of simply setting the center manually, and defaulting to 0,0. My idea was to open a window that has the pixelated version of the map in it and showing the center, as well as the outline of the area that would be screenshotted. Unfortunately, the game does not allow to draw on map elements like that. This is also the reason why the area for the area screenshot is not drawn when the map is pixelated. Without this very user friendly approach I have no idea how to do this without being veeeery unintuitive. I could show a bunch of numbers like "chunks left to the chosen center" for all four directions, but that would still be very unintuitive. Also, this would require manual work, which is tedious.
Last but not least, one of the challenges as a coder that takes feature requests is that what a user says they want is very often not what they actually want, as it is already quite merged with their initial approach. You say you want a way to manually set the center of the screenshots, but I think your actual problem you want to be solved is misaligned screenshot centers.
Solution idea
After thinking about your input for a bit now I think the best approach would be a combination of my second and third approach.
The center of the screenshots will start at the center of all generated chunks. Every time screenshots are started an additional check will be run if a screenshot would be empty on more than 20% or so to one side of the image. If so, the image would be centered based on the base limits again. The check would be necessary a second time for the other axis as well.
There should be certain rules and settings:
* never zoom back in once zoom was already increased, this would look... weird and jumpy in timelapses
* setting to lock the screenshots to 0,0, being on by default if upgrading from an older version of the mod to avoid breaking timelapses, whilst also warning the user about the new feature
* maybe a setting to change threshhold
* maybe an additional setting to truly be able to manually change the center
* a setting to zoom back in once entities were removed, which would reduce the base limits.
This might sound rather trivial, but it affects almost all parts of the mod. This feature will definitely come with 3.0, when I redo the whole UI. Before that I will only add the feature that the zoom will be adjusted if deconstructing of entities reduces the base limits.