Richard, you wrote “… the Center of Effort. was designed with the gunter rig to be just before the mast to give slight weather helm…” That is incorrect, and seems to indicate some confusion. To begin with, the “centre of effort” of your yawl sail plan is well aft of the mast, somewhere on a vertical line which passes through the forward half of your centreboard case.
Centre of Effort (CE) and Centre of lateral resistance (CLR) are both misnomers, as neither means exactly what it says. Both of these points are static centres, calculated by geometry, to act purely as a theoretical guideline to the designer. In real life, the centre of pressure of the combined sail plan moves around quite a lot, according to how the sails are trimmed – and even affected by how the sails are cut.
Similarly, the actual centre of lateral resistance of the hull also moves quite a lot, according to the angle of heel of the hull, how the vessel is trimmed, and (in your case) adjustment of the centreboard.
CLR and CE and how much “lead” (ie how far ahead of the CLR should the CE be placed), are matters of fine judgement (or guesswork) on the part of the designer, based on his/her knowledge and experience of that hull design and that type of rig. The goal is to find the best compromise in terms of helm balance – a small amount of weather helm in normal conditions if possible.
Generally, when converting a boat to junk rig, it has been found from experience that we can put the CE (the geometric centre) of the junk rig to coincide with about the same position (on a vertical line) as the CE chosen by the designer, for the original rig, unless practical knowledge of the way the boat handles, dictates otherwise. This normally means moving the mast forward, to allow the two sail plans to have coinciding geometric centres.
Your case is a little different because (a) you wanted to keep the mast in its original position and (b) your original rig is yawl, which means the main mast is already a little further forward than it would have been if it were a sloop.
Arne has taken advantage of that, by putting a suitable junk sail on the existing mast position, leaving the mizzen sail out of the calculation, thus achieving a CE position approximately where it was originally designed to be (just a little smidgeon forward actually, but he knows what he is doing). The mizzen is no longer needed and there may be times (eg heeling in a strong breeze while hard on the wind, with the centreboard fully down, when the addition of a mizzen sail might create too much weather helm – although that remains to be seen.) As Arne says, since you already have it, why not try it anyway? There will certainly be some points of sail, when you can raise the centreboard and shift your weight aft a little, where the Johanna sail with the mizzen also pulling, could balance very satisfactorily. You have a lot of flexibility with a dinghy and these CE and CLR things are not tyrants, only guidelines for optimal conditions. If you follow Arne’s advice, and add some practical experience of your own with regard to sail trim, use of centreboard etc you can probably have the best of both worlds, even if there are occasions when your first reef will be to drop the mizzen – in other situations it may well earn its keep.
As I tried to explain before (I didn’t explain it very well) if you want to keep the mizzen AND utilise the main mast in its current position AND still have approximately the same CE/CLR relationship, then you will need to have a junk sail with more than normal proportion of its area ahead of the mast (high balance) and the most extreme in this regard, which is also well proven, is a SJR sail (split junk rig) with 33% - 35% balance.
You have flexibility with a dinghy and either option would be satisfactory, I think. I happen to like the SJR solution, but Arne’s suggestion would be just as good – maybe better – there is still nothing to stop you from experimenting with the mizzen sail and enjoying its special advantages (heaving-to etc) if you want to. You will soon find when it helps and when it doesn’t.
As for engineering the support for a free-standing mast – it’s only a dinghy, for goodness sake. Just fix the heel of the mast on the keel, and make sure the thwart is robust enough and fastened well enough to the hull, with proper knees, so that the mast can’t rip it free – it’s not rocket science. The higher from the mast heel is that “partner” support the better – if you are concerned you might mount a thwart at gunnel level. The distance from the mast heel to the thwart must be no less than 10% of the length of mast above the thwart, is the usual rule of thumb, and the more the better. What's the worst that could happen?