Your analysis of the court system problems rings true to the issues I hear about. When cases are rescheduled, often to 2+ years in the future, it's because they couldn't get a prosecutor, judge, clerk and court room together. One missing piece and the defendants are sent home at the end of the day.
Yes that does seem to be at the heart of the issue! And for every trial cancelled on the day for that reason, there will be others which just take longer to get going, so you get fewer hours of actual hearings in the day.
I think judge-led trials would be a bit quicker than jury trials, bc while the same arguments and evidence are presented etc, judicial instructions to jurors seem to be increasingly complex/lengthy, & jurors tend to get more breaks over the day than judges. Some evidence on this from Australia