In terms of the gap between 1x03 & 1x04 it shouldn't be more than a day or two. The body is still in the morgue and the technician is clearly giving him information close after the incident if there isn't a police report for Matt to follow up on. Also his niece hasn't seen him yet. I would guess 24 hours post 1x03 to allow time for discovery and the morgue technician to do his thing.
If this does end up shifting things to February (which ill wait and see for whenever the St Paddys reference is) I personally will just increase the court trial time as google is telling me that average murder trials last weeks up to multiple months and so I would prefer to show that more accurately which I think would also help space some stuff out in Jan before any February dates IMO.
