I'm skeptical of "full market value" for unique items for which there is no public market.
If you, as a finder, disagree with the valuation, you can “send your own valuation for the committee to consider”, which sounds like an interesting process to navigate. I imagine you’d have to find a credible alternative buyer who’d be willing to pay a higher amount.
[0] https://www.gov.uk/government/organisations/treasure-valuati...
[1] https://www.vcoins.com/en/coins/ancient/roman-coins-2.aspx?c...
Pretty much by definition, its "full market value" cannot be determined by a committee.