My dd (also 8 months and also Claire) gets 9 oz during the 9 hours I work. She takes 3 3oz bottles. She has always been fussy at the end of he bottles but since she was gaining well I never worried. She never fussed after nursing.
I called a LLL Leader and her suggestion to switch to an even slower flowing bottle nipple did the trick. Baby now takes longer at the bottle and is happy after.
Also I pump 4x during my work day for 3 bottles. I get between 2 and 3 oz per session.
Bottom line - your experience sounds very similar to mine and very normal.
Unless a doctor is expressing serious concerns about your baby's weight gain (and even then!!) supplementing is probably more detrimental than beneficial.