What's his alibi? His lack of alibi is certainly a big problem.
So you would convict him on:
1) You think 11pm dinner is a lie.
2) You think sleeping-in alibi is a lie.
3) You think writing in his diary about the knife is a very irregular lie.
4) You think the bloody footprint is a clear indication of his presence.
5) His testimony to the police on the night of the 6th, when told by the police that there was definitive proof placing Amanda at the murder scene that night, his statement that "his previous testimony was a load of rubbish" and that she must have left that night, is conclusive proof of murder.
6) He said he hoped Rudy didn't say "strange things" about him.
7) His computer records showing he watched a movie ended at 9:10pm. Then there is another record at 1am, and another record showing he played music at around 6 am. His other computer drive was fried. The gaps in these records gives him time to be at the murder scene so he has no alibi for the night of the murder.