..., beginning on March 23

Hello, everyone,

1-1. Starting in the new year, the new policy bans cars in the city centre.

I parse ‘Starting in the new year’ as a participle clause modifies the subject of the main clause and adds information about it, on which, I think, everyone will agree.

However, when a participle clause is placed at the end of a sentence as follows, the analysis of the function of this clause seems to be very complicated and confusing to me.

2-1. A health warning will appear on all liquor bottle, beginning on March 23.

2-2. I'll save money, starting tomorrow.

I assume the function of above two clauses would be the same and one of the following three possibilities;

A) a participle clause,

B) a reduced relative clause (= “A health . . . all liquor bottle, which begins on March 23.” And the antecedent is the whole main clause.)

C) a marginal prepositions (=a participial preposition like considering, following, given, including, regarding, etc.)

While I’m inclined to B), I’ll really appreciate on your valuable opinions.