John Kelly - thanks for this enquiry.
First I should note that neither I nor anyone else can give you an 'official' view on your query , as it is only in the Scottish Courts that you can get a definitive judgement on matters of interpreting law as you request. I can give you some pointers, which may be some help, but is no more than that really. So the below is just an informal discussion ..
Archery as you describe is obviously an activity with a 'recreational purpose', so might appear to be within access rights. However, in my reading of the Act, it is section 9 (c) of the Act which is the crux here. Section 9(c) excludes from access rights the activities of "hunting, shooting or fishing". There is no further definition of 'shooting', but I would expect the term might reasonably be taken to encompass the shooting of arrows as well as of bullets. So this 9(c) provision would put archery outside the exercise of statutory access rights. - probably not the answer you were hoping for I'm afraid.
We did have some discussions soon after the Act came into force with Field Archery interests in East Lothian. However, the issue there was that they rent an area of fields and woodland which they use for Field Archery, and were looking for guidance as to how they could warn any members of the public who - using their access rights - might come into that area while shooting was underway. Therefore, those previous discussions with archery interests arose on the basis that archery was not carried out under access rights, but rather that the archery was an existing land use, on land which they rented. (We helped them draft some signs and warning methods that could be used around the site boundaries, to make access-takers aware of that activity when it was in progress).
As I say, probably not the answer you were hoping for, but I hope that may be of some assistance?
regards,