I really don't see what the fuss is about with dice rolls using multiple dice. Any realism advantage can also be obtained by carefully writing out your guidelines ('binomial' systems like Shadowrun get a break here, because they have other advantages).

I'm also not sure whether or not there is a need for the two ability scores rule.

It also doesn't make too much sense to throw the established core mechanic out of the window.

Using mod. + training bonus as opposed to mod. + 1/2 level + training bonus seems like a good way to handle things. Possibly allow the Training Bonus to add up to +10 as opposed to +7