Do yourself a favor and get the
Taylor K-2006 test kit. It is much more accurate than test strips (see
this post for more details). You do measure Combined Chlorine (CC) in addition to Free Chlorine (FC), but in a properly maintained pool or spa you will find the CC level to be very low if you measure before your soak (it goes up during and right after your soak, but then drops back down within 24 hours).
Note that if you have an ozonator but do not soak frequently (i.e. less than twice a week), that the ozone will react with chlorine increasing chlorine demand. You will need to add chlorine every day or two in that case, maybe twice a week if you add more. On the other hand, if you are using the spa frequently, every day or two, then an ozonator will help to oxidize bather waste and lower chlorine demand. Such high usage also works well with chlorine since you just add it right after your soak such that you have at least 1-2 ppm FC measured just before your next soak.
You might consider using the Dichlor-then-bleach method if you want your water to last about twice as long and have less risk for disinfection problems, but you would probably need to get your Total Alkalinity (TA) lower, perhaps down to 50 ppm, and would need to use 50 ppm Borates such as in Proteam Gentle Spa or a boric acid product or a combination of 20 Mule Team Borax and Muriatic Acid (or dry acid but that increases sulfates).
Why are you wanting to switch away from using bromine?