You have inquired as to whether a graduated contingent fee (the percentage payable to the lawyer changing at various stages in the representation before the funds are generated) is permitted.
Your concern is in all respects similar to that confronting any attorney. That is, while it would be wrong to defer settlement to recover a higher percentage, it would be equally wrong for an attorney to defer settlement so that the file can continue to be billed on an hourly basis.
In that sense, there may often be a conflict of interest between the lawyer's own (short term) economic interest (in either a higher percentage free or more hours billed on the matter) and the economic interest of the client, who wishes the matter resolved as cheaply as possible. The overriding issue is loyalty to the client.
Rule 1.5 appears to specifically permit graduated percentage agreements. Subsection (c) thereof states in pertinent part as follows:
... a contingent fee agreement shall be in writing and shall state the method by which the fee is to be determined, including the percentage or percentages that shall accrue to the lawyer in the event of settlement, trial or appeal, litigation and other expenses to be deducted from the recovery, and whether such expenses are to be deducted before or after the contingent fee is calculated.
In our view, use of the phrase percentage or percentages contemplates that more than one percentage may apply to the same representation.
At the same time, a portion of the comment to Rule 1.5 is appropriate:
A lawyer should not exploit a fee arrangement based primarily on hourly charges by using wasteful procedures.
The same would apply to a graduated percentage fee arrangement; it should never be exploited to the lawyer's advantage.
Therefore, subject to the caveat expressed in the quoted comment to Rule 1.5, your proposed graduated percentages does not appear to violate the Rules of Professional Conduct.