I always thought the right to a 'speedy' trial was more about latency than throughput. I.e., the accused shouldn't have to wait 10 years before the trial begins, but no guarantees about the duration of the trial.
It's easy to screw defendants over either way - say, "start" your trial ASAP...but then pause it for a few months for some quibble, then a few more months for some detail, then a few more months for ...
How speedy is speedy anyways? IIRC, the big reason plea bargains get accepted is because the offer is "time served" as-in the time you spent in jail awaiting trail will be what you agree as a punishment and you'll be immediately released.