What is an extended time? I never ran into this because we don't have subs. We have 8 man rosters for a 5 man team. At the end of the half they must have bowled 9 games for the roll off and 18 at the end of the year.
USBC has lots of rules but when you have a question you might as well get a magic 8 ball. Their search is awful.
Maybe you can drop the bowler and add another then see if they will let you drop the new one and read the old. So many leagues have rule that affect the bowlers. Probably why they have problems keeping full.
By the way I have never seen any rule that covers your problem.
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