We just faced this issue as we went to Hawaii.
After doing BBB for a few months, I became pretty comfortable with how my pool water "acted" over a period of days. I found that I could predict with reasonable certainty that my pool would lose "X" ppm of FC a day and the pH would rise "Y" every three days or so. So, I had the neighbor's son come over every day and add a predetermined amount of bleach and every three days, he would add a predetermined amount of muriatic acid. I showed him how to safely handle the chemicals and distribute them. It was my "best guess" of how to handle things and it worked out fine. We were gone for 10 days and I checked the chems when we got home and everything was A-OK.
BBB makes this sort of thing really easy to do. With TFP, you learn what happens in your water and why it happens. With those concepts in place, your pool water is predictable for the most part, barring any unusual things like excess rainwater or weird contaminants being introduced into your pool.
Keeping a log of your test results and what you did to adjust things helps you predict things as well.
You could leave a trichlor floater in there while you were gone, but your CYA will rise unchecked and your pH could still get out of whack. Best to have someone to watch over things. A responsible neighbor or neighbor's teenager is a good way to go.
Good luck!