Well, you might want to reconsider after Petsafe tells you how much they want. Personally, this move was a big part of my decision to move most of my flying to AA/OW from UA/LH, after 19 years with Miles and More...

I'd try to get them used to a carrier in the meantime - a few long drives should give you a good hint on how they will behave on a flight.
You can do a mix - carry them on on the UA flights, and check them as baggage on the LH flights if you feel uncertain about how they would handle being in a carrier in the cabin for so long.
In case the FRA layover exceeds a certain time, AVIH pets (AVIH=checked baggage) get transported to LHs animal lounge (same facility LH uses for animals shipped as cargo), are fed, walked and cared for there.