Rather than the Man in Seat 61, use the German Rail Schedule and Fare webpage.
Even if you try to book at the earliest date possible for Savings Fare tickets, you might not find the lowest possible fares available. (I'm not sure if the lowest possible fares, and how many at that price, are actually offered for some popular routes and times.) If you can't find low enough fares, there are several other possibilities.
Select "All excluding ICE" under means of transport. You'll find several less popular connections, such as direct ECs from Frankfurt to Munich. These trains take 40 minutes longer, but often have lower fares available.
If the fast train lower fares are no longer available, the difference in price might make it sensible to take the slower regional trains. Anyway, you might want to stop over and see Würzburg on your way.
On weekend, the lowest fare is, at this time, the Schönes-Wochenende-Ticket at 44€ for two. For a workday, instead of a 52€ QdL-Ticket, you can buy a local, RMV, ticket for Frankfurt Hbf to Kahl, the first stop in Bavaria on the RE to Würzburg, for 8,25€/person and a Bayern-Ticket for Kahl to Munich for 28€ for two, 44,50€ for the trip. Take any hourly RE from Frankfurt Hbf to Würzburg, as long as it leaves Kahl after 9 AM. In Kahl, you don't have to get off; just change tickets.