AA baggage allowance on mixed class itinerary

I've booked Key West to Palm Springs first class on AA, the best routing is to connect in MIA and DFW. However the first sector (operated by Republic Airlines on an embraer) is economy as no first class on those aircraft. My confirmation seems to base the baggage allowance on that initial40 min flight. It states first bag is free whilst second bag would be GBP22.10 & third bag GBP94.70. Does anyone know if in fact these charges would be waived given that two out of the three sectors on the through ticket are first class?

Thanks
James

ISTBC but I believe you're entitled to the first class allowance on all sectors if you've bought a first class ticket but first isn't available on one of the sectors.

We flew BA to MCO via JFK in PE and then down to MCO with AA last month and the baggage allowance was the greater ie BA allowance on both flights, likewise coming back with the internal flight with US air and the 2nd leg with BA again the larger BA allowance was applied on both flights.
Hope that helps

Thanks guys for your replies, looks like we'll be fine

The only thought I would have is if you want to take 2 carry-ons onto the first flight... Make sure one of them has all your electronics & valuables in and the other one that can be gate-checked if space in the overhead bins is tight.

I know Embraer say the bins on the ERJ-175 can take full size carry-ons - but I think a lot of us have seen what some [mainly] American passengers consider to be a full-size carry-on.