Legal time to review a multi-year history is the main item, and it is more substantial than an initial eligibility check because the record is longer and the analysis heavily fact-based. Add record retrieval, any document ordering, and the cost of preparing whatever route the advice ends up supporting.
Separate the review from whatever follows
Ask for the history review to be scoped and priced on its own. It may conclude that no further United States assignment is available, in which case the remaining budget should go to relocation rather than filings. If the review does support a next step, the preparation cost can then be assessed with real information.
Confirm any government charges at the time of the relevant step. Hypothetical example: a specialist in the organisation's kiln-control systems asks for a full options review at the same time as the history reconstruction, and pays for advice that the record then makes irrelevant. A first review would have completed the inventory first and priced it separately, since the inventory determines which options are worth analysing at all.
Ask for the history review as a defined piece of work with a written output, and agree what happens to the remaining budget if the conclusion is that no further United States assignment is available.