The starting point for analysis seems to be Fla. Stat. 765.205: "The surrogate shall . . . provide written consent using an appropriate form whenever consent is required, including a physician's order not to resuscitate."
Approach One takes the statutory language literally and requires not only the surrogate's consent but also the surrogate's written consent for a DNAR order. This is not an ethically preferred approach, since it places a heavier burden of decision on the surrogate. Moreover, this is a statute about surrogate duties, not clinician duties. Later Florida POLST legislation suggests the statute really means only that the surrogate must provide written consent when written consent is required (and following the applicable decision making standards the surrogate agrees with the proposed treatment).
Approach Two requires the surrogate's consent but not the surrogate's written consent. But this approach still requires the clinicians to ask for the surrogate's yes/no authorization for a DNAR order.
Approach Three requires only the surrogate's assent. On this approach, the clinicians announce what they plan to do, namely write a DNAR order. They are not asking the surrogate. They are telling the surrogate. But during this announcement, the surrogate still has the opportunity to object.