Three concepts to keep in mind: Financial benefit, choice and insurance.
1. $$ benefit. Figure out an approach showing them the $$ they might gain or lose by changing over. It probably will take a 3- or 5-yr time frame for this. Don't forget to include the value of enhanced operational (not just financial) reporting from the new tools. I think billing these tools as just ""FRx replacements"" minimizes their real potential and value.
2. choice. What Wayne said. Present the options in light of (1), and in your take on longer-term potential of each tool. Make part of the choice doing only the more valuable reports, and the leaving the rest in FRx for future decision.
3. Insurance. Treat the conversions not as per-report, but for the lot or sub lot. Like insurance, you know you'll spend more than planned on some, but less on others. Maybe break the reports into 3 categories (ez, med, hard) and price them per report class. If the customer wants to reduce cost, he'll leave some in Frx for later. It might also flush out some of the customer's true value in the reports, when a hard report isn't perceived as actually being worth it.
Wayne's comment I think implicitly reminds us that we have a tendency to make decisions for customers. Part of our value is to help organize the problem into a form that makes it easier for the customer to see his choices in a way that they won't regret the decision later (not blame us for it if unhappy.)
Also, if I were in your shoes I'd figure out how to organize a simple consulting proposal so that the customer pays for the analysis of the problem FIRST. He already rejected the 1st recommendation. Maybe apply the fee to the final project. It will, at the least, get their attention that this is not some simple ""sales"" problem for them.