In the morning...

I wake up with more milk than she is willing to drink. However she seems to really want to cluster feed at this time. Maybe every hour feeds for 30 minutes. Anyway, as I lay here right now, I just fed her for a long while, layed her down, and am debating pumping for comfort. My fear is that by the time I drain my breast with the pump she will wake for more. Do I just deal with the full breast for an hour or two so she can have plenty to drink later?