Paul,
everything is doable, but the impossible jobs take more time .
I can see two ways:
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A broad sail can be made to get the CE right. That will require new and serious rudder, preferably a swing-up or haul-up rudder which in its low position is around 120cm deep. That is OK if 95% of your waters are deep enough.
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The other way is to just move one of the shown sails forward, and then bring the total CE aft with a simple triangular mizzen, set with a sprit boom and sheeted to a not too tall boomkin. The mizzen rules out a windvane, but it will in itself act as one, except when sailing downwind. The mizzen will also be a fine riding sail when at anchor. With the main moved forward like that, the steering downwind should be fairly easy.
This setup, with a jigger, will let jo have a rudder of the same draft as today, but I would anyway advise you to add a pair of endplates to it. In case you make a new rudder on the transom, the rudder should also be given a pair of 'anti ventilation plates' near the waterline - identical to the endplates.
I strongly recommend Karlis Kalnin's article on rudder in JRA Magazine 74, p.26.
Since it is raining horizontally here, at only 8°C, I can just as well have a look at it.
More coffee...
Arne