IMO assault engies don't justify their cost outside of laying demo charges. Yes they deal massive damage at point blank range, but the opportunities to get into that range without losing a model is pretty scarce. You really have to ambush around a corner to use them effectively as most competent players will just focus them if you try to charge.
Thompsons on vehicle crews just seems like a wasted slot in your commander tree.
Assault engineers can feel as a random experience, sometimes they just die like flies trying to close the distance and sometimes they just spank enemy squads.
I've tried to learn to use them more effectively lately and the only thing I can recommend is try to use them the same way you would sturm pioneers. What I guess you could try is this: First, use volks or riflemen to set up in any nearby cover to take fire. While they are acting meat shields, bring your sturm pioneers or assault engineers in from a different angle and close the gap, usually I right click and drag their positions right next to the enemy unit.
If all works like it's supposed to, the meat shields will take the bullets while your burst units close the distance in relative safety and cut down the enemy unit.
The problem with this is that if they switch targets to your AEs they are toast. The only way this works is if you are already close before you start your flank.