a judge would have accepted. He's not lucky, it's just the circumstances. The officer doesn't have to have evidence to issue a warning, so they are allowed to guess the speed.
Your best option is to go to the court, ask what would happen if you plead no contest and try for a deferred sentence with stipulations like traffic school or 90 days no tickets. Talk to the court clerk, they usually can give you an idea of what to expect when you contest the citation. They cannot give advice... but it's the next best thing.
Solo in the HOV lane, that could be a gift from the officer or there's history of judges in Utah dismissing those charges when it's clearly going to be an otherwise unused lane (11pm at night). Shame on the Utah legislature for not fixing that law to only require carpools during peak traffic hours.