I'm actually inclined to agree more with the pet store guy. 6 gallons is a lot of space for a single betta, I would do smaller water changes more frequently (meaning, more than 1x weekly), and then 100% with a gravel clean once a month. I have 2 female bettas in a divided 5 gallon, I do 20% water changes every other day (larger on Mondays- it's an office tank so they are on their own Sat and Sun) and once a month a full change with gravel clean (bring in my gravel vaccuum from home). They seem to be doing very well, they've been on this schedule for about 4 months. In my opinion, pet store guy did definitely have you doing too few water changes, but I don't think it's necessary with 1 betta if you're only feeding him a few pellets at a time to clean the gravel weekly.
I think you could do 20-30% water changes twice a week, and monthly gravel clean.
Within reason, it's always better safe than sorry with the water conditioner. Treat for the full 5 gallons anytime you do a water change, the extra conditioner won't damage the water quality or fish but not enough definitely could.