As I said in the last post, you can work it out for yourself. If you do, I think you'll be surprised.
You can pretty much figure it out for yourself. Just work out how much angular momentum the Moon gains as it climbs away from the Earth and compare that to how much angular momentum the Earth loses in the same time by its slowing. Both these rates are well known.
I don't think you can simply take the difference in these two numbers and say the difference is from radiating the waste heat of the tidal process.
Here is my reasoning:
1. The dissipation/radiating takes place near the Earths surface. Even at the equator the spin speed is a very small fraction of the speed of light, so the redshift/blueshift effect has to be very small. (If all this radiation was directed East, the effect would be some 650,000 times greater)
2. Any difference would be much more due to absorption/dissipation/re-radiation of solar energy hitting the Earth...still related to v/c for momentum, but the energy exchange of solar is (50,000 times if my sources are contextually correct) many times greater than tidal.
So I am thinking the Earth would lose some angular momentum anyway, the angular momentum robbed by the moon is a much greater effect, but the angular momentum loss from dissipating tidal energy is almost insignificant in comparison.