We need to talk, because I have exactly the wheels you are interested in fitted to my Ace 2.6! Wheel arch clearance is tight at the back, my car is Ok but individual bodies do vary. The wheels are shod with 70-series Avon ZZ tyres (about half worn). These are beloved by Healey drivers, for good reason, they really are excellent tyres. I am interested in changing for three reasons: firstly the combination of 70 series and 15 inch lowers the gearing, and my car does most of its miles over long distances. Second, because I have Cobra box sections at the rear the exhaust is lower than a standard Ace, so I need all the ground clearance I can get, and thirdly the lower ground clearance means I can't get the standard jack under the chassis tube at the back, though the front is OK.
For all these reasons I am thinking of returning to 16 inch wheels, though I wouldn't want your 4 inch rims. My plan was to wear out these tyres first, but I could be persuaded...