Hi.

You already got some good answers...
I feed a 20% flock raiser to all my birds with oyster shell available on the sides... chicks, layers, rooster, breeders, grow outs. It is the easiest way to feed a multi age flock. And as noted by others does not contain excess calcium that could (doesn't mean will) lead to kidney failure long term in some birds.
You have already established 15% is too low, and I agree. But there are some variables like breed and access to other stuff. Larger breed birds need more protein than lighter breeds. So you MAY get away with feed 15% to a leghorn LAYER but not a barred rock, and NOT chicks. True recommendation is not less than 16% EVER. Here is a link, note one type o that say 5-17% should say 15-17%...
http://ucanr.edu/sites/poultry/files/186894.pdf
Too low of protein will cause all kinds of behavioral and health issues. Slightly higher (as in 20-22%) will NOT, but give you a little leeway. (above 25% is usually gamebird feed and would be too much long term as well). Those who wish to feed organic but not layer must feed organic starter. Or at least I haven't found an organic flock raiser. Note, it's the amino acids in the protein that are important. And feathers are made up of 90% protein.
I wouldn't get rid of the rest of your feed, that would be wasteful. Mix it with your new bag.
Easy on the eggs, they are also high in fat. I feed them as a treat. Peas are a great source of protein. Frozen if it's hot out. What's also important is you AVOID scratch, it is candy bars for chickens and quickly diminishes protein level.
AS much as I like to buy into the whole rooster eating layer thing, I do see plenty that are even 6 years or older and always had layer. That won't be mine, but I make a personal choice not to feed them layer. Same way I make a personal choice to feed my birds more than the MINIMUM that layer is. It DOES cost me more, because protein is pricier than oyster shell, that is generally 4% of the bulk of layer. Shopping around for the best price (by internet or phone) has proven fruitful though. I pay $3.35 per bag extra if I shop local. But instead I buy when I drive past the store to see the in-laws.
Before you know it your birds will be all grown up.
I was surprised when I saw a "start & grow" buy Purina with only 18%. Grow I get, but start... Not on my $! They replaced a broiler "starter/finisher" feed that was 20% and this is supposed to be the replacement product... you bet, for the same price. Interestingly, both feeds were made by Purina, just under a different label.
Anyways, my lesson was read the nutrition label not what they "call" their feed!
Sounds like you've got it under control before any issues popped up. Good paying attention.