1. Your biggest consideration is what the trust says to do. If the trust instructs the trustee to transfer the house to the beneficiary, you need to put on your trustee hat & deed the house to the beneficiary, then put on your beneficiary hat & sell the place. If the trustee has the option, you should consider that the trust can write off various expenses such as tax prep fees, court fees, the costs of changing title from the trust to your name, etc.
2. AVM is available if & only if the AVM date results in a lower gross estate & lower *estate tax* liability. Whether it helps your personal taxes is irrelevant. AVM is available even if some assets go up in value, as long as the total assets go down in value. The 3 "arguments" you listed are incorrect understandings of the AVM rule.
You can declare the house was worth whatever you want when you sell it. But if you get audited, you'll have to convince the IRS it was worth $325k then, & hope the auditor doesn't ask about the appraisal. You'll have to judge the likelihood of an audit & whether you can successfully show the house was worth $325k at your mother's death.
FYI: if you're filing an estate tax return, you have untiil 9 months from your mother's death to do so. (You can file an extension if necessary.) Whatever value you put on the estate tax return is the value you'll have to use as your basis for sale.
This post does not constitute legal advice, nor does it create an attorney-client relationship. Postings are based only on the information provided and you should consult an attorney in your area before relying on information contained in this post.