Very good thinking. I read your note on counting for suppression after losses, and I liked it.
It would use that one as a special rule for elite troops, as the other very good ideas you had to make training a difference in combat. I always like to keep rules as simple as possible, and alway be symetirc. That is why I would use no D4 or D8. Stay with BF:E as long as possible.
In BF:E we have the civilians MEA, which have a special rule to represent their low training (excluding the 1D6 in CC). Your rule for high training add flavour to the game.
For the accuracy of bolt action: Use the Exterme Range rule. Do not reroll, but use D6-1. That will make the high punch and deadly accuracy of bolt action rifles count. And it will differ them highly from MGs.
The SMG rules are good. What was your range? 8 or 10 inches? Actually a SMG is a small MG. Therefore counting one damage die for two for suppression is justified. For SMG damage, 2xD6-1 is good, and a 2xD6 for the Thompson. The range will make the difference, and the high supression rate, which is both very fine in game terms.
Sten, PPhSh41, M3A1 and MP40 can all use 2xD6-1. No Extreme Range for SMGs. You can make the Sten use the Natural 1 Rule for a 1 and 2, to show its crudeness.
Pistols use the same stats, 8 to 10 inches and 1D6 or 1D6-1, as the calibers go.
With this set we would have sqaud MGs, bolt action rilfes, SMGs and pistols. Hand grenades are included in the rules. So we only need some mortars and some specialist weapons, like mines against tanks, multiple hand grenades against tank tracks (geballte Ladung), shaped charges against tanks and panzerfaust, bazooka and PIAT rules.
Then we can play WWII BF:E. . . very good idea of you guys. . . One of the most important impacts on the game would be The Old Soldiers special rules for training, and assigning them to theaters and timlines.