[Jim S]

Jumpmaster, what you are saying is pretty much what we do. The 'new' timing rules for varsity, and the 'old' timing rules for non-varsity.
Under the old rules you go with the RFP after changes of possession, including after a free kick, as long as the ball remains in the field of play. (I normally use this as the start of a 'faster' clock on blow-outs, It's the least obvious speed-up you can do.)
The rule on this question howver would be the same under BOTH sets of rules. The clock should start on the RFP. Just because there is a kick does not mean that for the next play the clock will start on the snp. There must be a new series for that to happen.