The rule works off a defined list of functions performed in the transfer, and the duty lands on the first person in that list who performed one of them. Being listed as the closing or settlement agent on the closing or settlement statement, then preparing that statement, then filing the deed with the recording office, then underwriting the owner's title policy, then disbursing the greatest amount of funds, then providing an evaluation of the status of title, and last preparing the deed. So in a plain non-financed transfer to an entity, the settlement agent is usually first in line, which is why the industry ended up carrying this. The parties on that list can agree in writing to designate one of them to file, and the designated party takes on the filing duty while the others keep proof of the agreement. Confirm the current text and the exact cascade order with counsel, because the language matters more than any summary of it and the compliance details can change.
Your worry about designation drifting to the least equipped party is the real operational risk. A designation agreement doesn't reduce anyone's interest in the report being right, and if the designated party doesn't file, you're the one holding a piece of paper explaining why you didn't. I'd only sign one where the other side already runs a program and you get confirmation of filing back in the file.
On intake, treat it as a data collection problem with a hard cutoff. Beneficial owner identifying information, the transferee entity details, the transferor, the payment method and the source accounts. Ask for it at opening, not at signing. Practices I've seen charge a flat compliance or reporting fee in the $75 to $250 range depending on entity complexity, disclosed on the settlement statement.
The part people skip is retention. There's a recordkeeping obligation attached to these filings and to designation agreements, so your document retention policy and your escrow file structure both need to change, not just your intake form. Non-financed includes seller carry and private money, which surprises people.