To answer the question of how to calculate the geometric centre of the rig (CoE) I suspect it doesn’t matter too much whether you include the overlap of the genoa or not.
The calculation is a little bit different, but there is a self-cancelling aspect to it too.
Out of curiosity I did a rough calculation using the diagram given by sailboatdata for the MG Spring 25 and assumed it is a proper scale drawing of the sail plan. (An assumption I have found to be wrong on a recent similar exercise). The exercise was also done roughly on a computer screen, no CAD software, so this should be taken as an approximate exercise.
The result, as I suspected it would be, was pretty much the same. The difference is within what I would consider to be the margin of error in my rough drawing.
I didn’t read the question properly to start with, and over-looked your description of the genoa as having a high clew, but that detail, if anything, would have made the results even closer.
Now for your other question, as to where the mast should be placed – that depends entirely on the type of rig you want – or (a more practical way of looking at it) you could place the mast where internal accommodation and structural details demand it, and by reverse reasoning, find the type of rig which will fit.
By type of rig, I mean, basically, whether it is a high mast balance (low yard angle) type of rig, or a low mast balance (high yard angle) type of rig.
To demonstrate I fitted (very roughly – Mk1 eyeball) two extreme rigs.
The Amiina Mk2 rig (split junk rig) has a mast balance of 33%, and I picked one of Arne’s Johanna rigs which allows a mast balance as low as 12 %. You will probably want a rig which is somewhere inside this range.
When the rig is placed so that its geometric centre lies on the same vertical line as your original geometric centre, you will see where the mast ends up. You can see from these two diagrams that the mast could be just aft of the hatch (if the balance is 33%) or just forward of it (if the balance is 12%), or anything in between – as the range of possible junk rigs vary between these two extremes (33% to 12%).
Your internal accommodation arrangements, and the presence of any internal bulkheads, will probably lead you to decide mast position, which in turn will dictate mast balance and over-all planform of the rig you choose.
The drawings, as explained, are based on the assumption that the sailboatdata drawing is approximately to scale, that the sail plan shown approximates to yours, and on the basis that my additions are not done with any great amount of accuracy but mainly just to demonstrate the idea. The result won’t be too far off the mark, but I suggest you do it all again yourself, preferably using CAD software and accurate measurements which you can get from your boat. If I have made any major error here no doubt this will be picked up by others who have more expertise than me, this will be enough for you to decide if you want to go ahead with the idea.
From your comment about the way your boat stands up in strong wind, you will presumably not try to add more sail area than the designer originally called for (and there is no real need). Arne has reported that his boat sails pretty well with just the top panels, so if you anticipate deep reefing, maybe one of the Johanna rigs will suit – there is quite a range of them if you look at Arne’s notes in the technical section of the website documents section. The split junk rig will suit if you want the mast as far aft as possible, you can read Slieve’s notes on the SJR which are also in the documents section.
Hope that helps.