You would only need a 2.45L starter if you were using a stir plate.
Your 6.53L starter size is if you make it and don't touch it at all (not advisable). Do a simple O2 at start and the size drops to 4.9L. Do some intermittent shaking (when you pass it, swirl it), and the size drops to 3.77L.
Bottom line, you'll need significantly larger starters if you make and do nothing with them. Give the starter wort better oxygenation/aeration (through different methods) and the size keeps dropping.
BTW, even before I had a stir plate, I would at least do the intermittent shaking/swirling so that I didn't need to make large starters.