Making Rules Grid-Compatible

I AM expecting to use my Project Kaiser 54mm toy soldiers on a table-top battlefield formed of 12x10 3in squares.
However, I have a lot more reading to do before I decide on the rules to use, but if I do use an already published set they do not have to be specifically designed for a grid.
In fact I will probably compile my own rules, but would not be surprised if they are heavily influenced by Neil Thomas's in  Wargaming Nineteenth Century Europe 1815-1878.

Wargaming Nineteenth Century Europe … the more I read the book, the more I like it

The key to using these rules would be converting movement and firing distances from centimetres to squares.
Thomas has loose-order infantry moving 8cm in difficult terrain, 12cm in the open and 16cm on roads; close-order infantry moving 4cm, 8cm or 16cm; skirmishers, who are not penalised for difficult terrain, moving 12cm or 16cm; cavalry moving 12cm, 16cm or 24cm; and artillery moving 12cm or 16cm (no movement in difficult terrain). In addition, infantry lose a quarter of their move if turning. Note that all movement distances are dividable by four.
Weapon ranges are 8cm for smoothbore muskets, 16cm for early rifles, 24cm for later breechloading rifles, 32cm for smoothbore guns, 48cm for rifled bronze guns and 60cm for rifled steel guns. Again all measurements are dividable by four.
Bearing in mind that Project Kaiser is for toy soldiers at corps level rather than regimental, and will work best with simple - but not simplistic - rules, I would probably dispense with skirmishers and just have one formation for infantry. None of my infantry will have smoothbore muskets, so their 8cm range can also be ignored.
One possible solution would be to convert the 60cm range of rifled steel guns to five squares. This would give rifled bronze guns a range of four squares, smoothbore guns three squares, later breechloading rifles two squares and early rifles one square (in each case distances have been rounded to the nearest whole number).
Movement distances could become one square for infantry in the open, half a square in difficult terrain and two squares on roads. Cavalry could move two squares in the open, one square in difficult terrain and three squares on roads. Artillery could move one square in the open and two squares on roads.
There has been even more rounding with the movement distances, and there is the additional problematic factor that infantry have a half-square move in difficult terrain.
But as movement would be measured through the sides of grids, rather than through corners - a point emphasised by Bob Cordery in his Portable Wargame books - there would be no need to give infantry an extra penalty for turning.
Inevitably there have been some compromises in the above conversions, but I think they make a good basis for further work.