I'm not sure I follow why this is more "non-partisan". I also don't follow your split analysis. I count 9 county splits in four counties, using the rule that districts entirely within a county are not a split piece. That's the same number of splits in my map.
The way I would count splits is to determine the minimum number of districts that must be included in a county, and then add up the population from any excess districts.
So if a county has less population than needed for a district, then you count the population of the smaller fragment(s). If a county has more than enough for a 1+ districts, you count beginning with the 3rd largest fragment.
Don't allow double spanning, where two counties are split between the same pair of districts, and limit the total number of county fragments to Ndistricts X 2.
The rule for house districts in the Ohio Constitution seems like a good idea, but probably forces more splits of smaller counties, because they can be arbitrarily split. And see the truly awful district joining a little bit of Mahoning, Stark, etc.
Even if a district is wholly in a county, you still have to delineate the district (postcards to voters, ballot printing, signs for district boundaries, etc.).
It is possibly an artifact of the old apportionment scheme where counties were given temporal fractions of representatives rather than spatial fractions.
A county entitled to 1.4 representatives would have been entitled to one representative for an entire apportionment decade, and a second representative for 4/10s of the terms (2 terms). Under the current constitution, the fraction is represented by a portion of the county joined to portions of other counties.