I am sorry but "its done more cheaply at FFD carriers" is just factually incorrect. First, mainline carriers don't fly RJs (the exception being AMR, Republic and JB) so the comparison falls apart unless you can make the comparison on a rate/rate basis for identical (or nearly so) airframes. Second, as was illustrated earlier, comparing mainline RJ rates to FFD RJ rates reveals near compensation parity (sorry General, when they negotiate a better rate at AMR and Republic we can have this argument again... until then they are still flying the ERJ for those rates and are thus subject to scrutinization). Do mainline carriers have higher hourly pay rates overall? Yes, but in general they also fly bigger equipment so it is only natural for them to have a higher rate. But again if you consider it on a $/hr/seat basis the FFD carriers are perfectly inline with compensation rates at mainline carriers. The exception would be FO pay rates which is disproportionately low on the FFD side and I would agree needs to be fixed dramatically. So, when put in the context of what began this discussion (i.e. ERJs should be flown by mainline pilots) everything suggests that the those rates, that don't exist at Alaska mind you, would be similar to those of a FFD counterpart, or roughly 1.25 $/hr/seat. Could this change? Sure, as General Lee said there are negotiations coming, but until then this is what you can go on and not be considered speculative. All of this does of course neglect none pay rate compensation topics (retirement etc.) But I leave that for another thread.
And I think it substantially easier to make the argument that mainline flying was "lost to" rather than "given/lent/whatever to" FFD carriers as you suggest, and the difference is not trival. As such nothing the pilots or management can do about it is a bit of an overstatement, otherwise it would have already been done.