They were having an argument. OP is on his prosthetics throughout. He wants Reeva to leave.
I suggest that he chased Reeva upstairs and she locked the bedroom door. He barged it to open it (the primary door would give, that's why he offers that information to the judge as he's using it in his lies) which leads to the marks on the second door, which probably didn't give because of the latch into the floor.
Reeva has the cricket bat to defend herself and runs to the bathroom with it (as he breaks the bedroom door open) and opens the bathroom window thinking optimistically that it might be a way to escape. Realising it isn't, she drops the bat in the bathroom and locks herself in the toilet. She has her phone with her.
OP is mad. He picks up his gun (or he already had it as he chased Reeva upstairs).
He screams "get the *advertiser censored** out of my house" at Reeva as he chases her to the bathroom.
If his first shot occurred at the earlier time and was followed by the three bat strikes (from the bat Reeva has dropped in the bathroom), that would account for the earlier sounds. Reeva is hit in the leg and falls, screaming at OP, and threatens to call the police. He sarcastically screams "call the police". OP looks through a crack caused by the bat strikes to locate Reeva and then aims the second set of three shots. The crack that deviates through one of the bullet holes is then caused by OP ripping the panel out. It is after this that Dr Stipp hears OP screaming "help, help, help" (which makes more sense to me than OP's version which he says is after the first 'bangs').
She dies quickly from the head wound as he carries her downstairs but is alive long enough to create the arterial spurts that are found.
Does this all work?