10 inch rims are officially for 11.2r24 tires.
So you already stretched your options on these rims...
If you found 11-24 rims (should be fairly easy to find), you could fit 65 series tires, which will keep the rolling circumference the same. 360/70r24 or 385/65r24 will fit those 11" rims. 12.4" is 315mm wide so you'll win 45 to 70mm in width.