I just did a little testing, and it looks like unnoting items doesn't count towards the trip count (only when going to the sawmill and the bank). What I did is I first chop tons of oaks at Draynor, then teleport to house with hammer, saw, money, and all oak logs (in notes). I also bring a fire staff, nature runes, and magic longs (in notes). I high alch while I wait. Have the servant unnote and go to the sawmill for you (the cook can take up to 16 logs each time). I then use those 16 planks to make it into 2 larders (which uses 8 planks each time).