If he felt any real remorse then he would fess up to honor his gfs memory and spare her family the bs. Having said that, I still can't believe that even in a rage he shot through the door knowing gf was on the other side, I'm just about prepared to give him the benefit of the doubt there. Having said that, it also seems clear that he shot through the door having given no prior warning to the 'intruder' to surrender, he is clearly irresponsible with a firearm, so yeah- murder, imo. At the very least manslaughter with the maximum tariff. Having listened to some of his testimony on the news and hearing about his past, I cant say I have any sympathy for him, in any case.
If it was an accident, then there is no punishment that will compare to living the rest of his life knowing he accidentally killed his girlfriend.
It is that possibility that has made me hold onto the every last shred of benefit of doubt for him, as I just can't imagine how awful that would be.