Although a chartered aircraft sounds simplistic for these volumes, if it is on a mainstream route (as this is) the group travel department of the major carriers on the route will often come in with a much better deal, using their established flights.

The issue with charters is that you are a "one-off", needing an aircraft to start at LAX and finish in Atlanta, and then some time later to do the reverse. A charter carrier is unlikely to have a programme where this just "fits in" at both ends, so there is likely to be some empty positioning to/fro, which pushes up the cost significantly, whereas a carrier with a major presence can accommodate you on scheduled flights. One-off charters can often be significantly more expensive than schedules, they come into their own for other reasons, privacy, obscure routings, etc.

Another thing about you being co-opted for this, be sure that you NEVER become personally financially exposed; you may like to consider getting someone else responsible for the money. With 225 travelling there will be some who pay late, some who won't pay at all, some who argue over the price, some who accuse you of pocketing any commissions, some who say they are not returning with the group and only want to pay half - the list is endless. A scheduled carrier is obviously better at handling a group of 225 that eventually turns out to be 200, or even 250.

Do try a broker, but don't be surprised if they end up offering scheduled group travel.