i'm not convinced by the 'milk has more calories than solids' argument. i think milk is very easily digested and doesn't stay in the tummy giving them that nice full feeling, while solids hang around for longer. if it were really the case that they should have lots and lots of milk and not many solids, adults would live off milk too.
i'd try upping her purees, i'd give her as much as she's happy to eat, and slowly try and string out her night feeds. try and make her wait 5 mins, and give her less each time, slowly so she doesn't notice, to wean her off night feeding.
i think part of the problem is that she's eating all night, so she doesn't need to eat during the day. i think you need to get the message across gently, that night time is for sleeping not eating.
my dd has just been doing the same as yours and i fed her during the night for 1.5 months, also starting after an illness. i thought she might need to catch up, which she probably did, but then got into the habit of waking for food. i've just weaned her off it now, and she eats well during the day.
another thing to consider is that eating at night can disrupt sleep. so i'd try and cut down on night food and increase day food.
hth