I took the front wheels off and felt the gap between the tire and the shock and the gap is about 10mm. The tires are 195mm OEM.
If I put 225 series tires on the overall width will increase by 30mm and assuming it will be evenly split between the inside and outside, 15mm of that will go toward the shock. Does that mean I will have to run 5mm less offset wheels with 3mm spacer? That will give me mere 3 mm gap.... Right? Wrong?
What do you guys do? The 225mm tires are for the track.

 

OK you have an R56 MCS with 16x6.5 rims and formerly 195/55-16 tires

If you use the same rims. Then yes the tires will be roughly 15mm towards the inside and to the outside.

What 225 tire do you propose?

Yokohama A048 in 225/45-16? I didn't find many 225 tires in 16" sizes that would fit. That tire is for rims 7-8.5" wide, perfect for 7.5" but your rim is 6.5" so do you plan to shoehorn it on? 23.8" tire diameter is ok.

5mm spacer could work.

See also 215/45-16, 215/40-16 or 205/45-16.