A guess why the school wants the money may be the whole tax-deductible issue-- namely, donating to a public school is usually a tax-exemption, but unless the money goes to the school, there's no accounting for it on the receiving end. You may be able to keep a separate account if you expressly state that the donation is not going to the school, but that may make some less inclined to donate, and you may have to pay tax on the account. (Note: I am in no way a tax lawyer)
One idea, short of making your team into its own 501c3: are there any non-profit education/community groups in your area? If so, and you're persuasive and they're nice, you can try to approach them about being your fiscal agent and a non-profit umbrella for your team. This could be useful if they're quicker and more accessible than your school. It's a stretch, but there's
one in my district. Just an idea.