I think if you add ammo dice one at a time, similar to the way Coriolis does it, it suddenly makes a lot more sense.
You make your base attack, but then you can freely add ammo dice one at a time to your attack, up to your RoF. Each dice rolled either shows additional ammo used, a bonus hit, or an explosion symbol. Matched explosions symbols mean something bad happened - like a weapon misfire, or you lost discipline and used up all your ammo. Additional hits are exactly as per the rules as written.
This is only a very minor mod to the rules as written, but feels more interactive: Instead of rolling all the ammo dice at once, you add them one at a time.
Also, I would not count the additional hits as using 6 ammo. I think the benefit of the additional hit should not automatically cost you 6 shots(yes there's a small chance of rolling amazingly well but not expending additional ammo, but I can overlook that). Instead I would say additional ammo dice use up 1 ammo, OR whatever number you rolled, and remove the '6' value from the hit side. For weapons with burst fire, each additional dice should just cost you the burst amount of bullets (eg. fixed 3 per dice)
For example: I miss on my base attack roll, but want to nail that sucker so I keep firing on full auto: I add an ammo dice - roll a 3 so mark off another 3 bullets used. I roll another dice, but roll an explosion. I'm running the risk of something bad happening if I roll another one, but I keep firing. This time roll a bullet - so I hit the target for base weapon damage. Conceptually this can be though of as missing on the initial aim, but walking the bullets onto the target, winging them.
You could even get more sophisticated, and say with CUF A you can add ammo dice one at a time, but with CUF B you must add them 2 at a time, and C or D 3 at a time. This represents greater control with higher CUF, and being aware of whether or not you landed a hit or just kept on firing regardless. Just a thought.