You should cater your raise amount to the size institution you pitch. You should have 2 raise amounts -- a 9 month plan, and a 24 month plan. Your 24 month plan raise should be at least $3 million or $4 million. For Vc's that have at least $300m or more under management, or any CVCs, you should say your 24 month plan raise amount.
VC's will determine your stage based on how much you are raising. You are self-canceling yourself from funds by asking for too little. It's easier for larger funds to write larger checks -- they need to deploy a certain amount of cash per year, and it's harder for them to write a small check.