If you check with your water utility, you may find that an RPZA is required and must be annually inspected as is the case for most irrigation systems using municipal water.

If not, why would the low clearance keep them from functioning properly?

Fist to understand the operation of a backflow valve. There are basically two types, that work on the same principal. In one a ball is designed to close the opening if the water goes in the reverse direction. In the other that functions the same except the ball is replaced by a flapper.

The only reason that the backflow valve is above ground is so that it can be inspected.Without the need to inspect it could be underground. While one valve would be adequate, If it was on the main feed to the irrigation system, there may be multiple valves if each leg of the irrigation system comes from a different feed. However the local regulation may change what is required where, so before you make changes make sure the changes area going to meet the local code.

I have 8 zone Anti-siphon irrigation valves from Rainbird. In the manual, it says it needs to be 6~12” above the highest sprinkler head in order for anti-siphon function to work properly.
If my understanding is correct, in california you can have an underground valve but then you would need a backflow preventer in this case. Or you can have an anti-siphon valve above ground with greater than 6” of clearance.

Ask the local atthority for a list of approved inspectors then hire one instead of trying end-arounds with something you don't understand.

Put the back flow preventer on the main line. Individual station valves do not last forever and I would consider the need to raise above ground anti-siphon Rainbird valves crap to begin with. They will have to be replaced one by one as they fail. It's not worth the effort to raise them all. You can switch to underground valves you don't have to look at when they need replacing.