Have you considered taking BP medicine in two half doses twice a day? In other words, if you are prescribed, say, 100 mg of a medication, then take 50 mg in the morning and then 50 mg before bed. This works for me as I seem to metabolize the medication quickly so that it doesn't remain in my blood stream for 24 hours.
Are you staying hydrated during the night? There's information on the web about dehydration affecting your kidneys causing them to retain salt thus raising your BP.