Actually there is no such thing as “centre of effort” or “centre of lateral resistance”. Both are theoretical points which, in the real world, move about as sail shape and hydrodynamic conditions change.
If you have a reasonably accurate drawing of your hull profile and sail plan, you can find the position of two points, which are: the geometric centres of area of the sail plan and of the underwater profile. (Including or not including the rudder??) They are not centres of effort and lateral resistance – if they were, you would simply balance them. They are merely a guide which can be used together with past experience, and knowledge of the type of hull and the type of rig. With a boat like the H28 whose characteristics are well known – if you are designing a rig of a well known type – then someone with experience could fairly confidently use these guides and tell you where the mast should go. Even matters such as the amount of camber in the sail can be taken into account.
If you were pioneering on your own and had no other option, working through the Hasler-McLeod PJR book is what you would have to do, and it is a good exercise anyway. In that case I would certainly also study Arne’s guide to junk rig design, which is on this website.
However my suggestion is, after that, narrow your sail preference down to a couple of planforms and then consult with people who have experience, preferably designed or specialised in each of those planforms. I have suggested at least two different types, because eventually it will lead to the decision of where the mast will go – and that might or might not be the deciding factor for you, you might need a choice. There are well-known experts on this forum (and I think they really are experts) who have been very generous in the past in giving this advice.
I am not one of these people, but I can see where you are at. Unfortunately there don’t seem to have been any other H28 conversions in NZ, for you to copy. (I am sure there will be in the future as there are plenty of these H28s around now, of an age begging for conversion.) So you are pioneering to some extent, but not by much as there is plenty known about this hull type. I would study the on-line forum discussions which preceded the final choice of rig for the already-mentioned Francis H.
A couple of points to consider: If you go for a so-called “conventional” planform you may have the luxury of fine-tuning after the rig is complete. This has been hinted at by David. It is possible to alter the mast rake, at least from vertical to anything up to 6 or 7 degrees forward. If you do a drawing you will find this shifts the centre of area of the sail considerably, so it would make sense to plan for a moderate forward rake, with a view to altering the rake fore or aft a little if necessary. The other luxury you will have, I believe, is the ability to sling the sail a little fore or aft in relation to the mast, in order to get the helm that you like.
With split rigs (at least SJR and I presume aerojunk) you are pretty much restricted to a vertical mast, and no ability to alter the position of the sail on the mast. So if you get it wrong, you will have to alter the mast position – or alter the underwater hull profile (not impossible, by the way, commencing with the rudder, but that is not going to be necessary in your case.) Also, Arne has pointed out situations where, if all else fails, a small jigger sail can compensate for lee helm – but again, I do not imagine for one moment this will be necessary in your case. Don’t try to do it on your own, consult with someone who has experience with that rig and that type of hull and can confidently advise you. Put a proposed drawing up on the forum and invite comments.
With some trepidation (because I don’t have any accurate drawings of hull profile or sail plan) I have opted for SJR – and the structural work I am doing, for the new mast position, is going to allow for a possible small shift in mast position if it proves to be necessary.
I am keeping my fingers crossed, and here is the good news for SJR: based on a remark once made by Slieve (who pioneered this rig), it seems that with SJR a reasonably good rule of thumb is to simply make sure the centre of area of the proposed SJR sail is about in the same position as the original Bermudan sail plan centre of area. In that case, together with the slightly more forgiving full keel profile and your decent sized rudder, you should be OK and don’t need to be chasing your tail worrying about percentage lead etc. If you do that, (just use the existing position for centre of sail area), and do the drawings, as I have done, you will find that your mast will be forward of where it is now – but not as far forward as it would be with, say, one of Arne’s sail plans, together with Arne's advice as to where the centre of his sail area should be positioned on your hull. (I found that a very heavy forward rake of mast on a Arne rig will actually leave the two mast positions fairly close). Depending on your internal layout you will then be able to choose what suits you best. And from there on, you will be able to work on your drawings and discuss with people who have experience in designing your particular rig. (And in my opinion it is no big deal to shift a hatch if that is where the mast needs to go. Also with the fore-body of your H28 you will not have a problem getting "sufficient bury")
First: go sailing on a proven successful junk, and have a good discussion with David Th.
PS I forgot to add: when fitting your preferred junk rig into your existing accommodation, it may help to know that the mast does not necessarily have to be positioned on the centre line - for the little bit of difference it might make, that is little more than just a cultural preference (a point Annie has well made in the past). It is more important to have a convenient space below, especially up forward, and not unusual for junk masts to be offset a little. Another one of the advantages of a free-standing rig. Annie: that takes it up to 54?