To be honest, it seems that most of the original Bradley scores exist somewhere. "The Early Bird Dood It!" is apparently one of those that exist from the original Bradley's recordings, that after they used for the international dubbings, so that's why that piece sounds different. I can tell that, because recently I found out that also the "Red Hot Riding Hood" original score exists, it was used for a Catalan dub of "Blue Cat Blues", and I sincerely don't know why since the instrumental track exists for that short. This can explain why there is no international dub that used the instrumental version of "Red Hot Riding Hood", because (apparently) it's the original recording of the first version of the short, in fact it contains the full Red's song (you can listen it here
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In essence, it seems that the instrumental tracks of the MGM cartoons already existed at the time, and were probably used in countries such as Spain as early as the 40s for some dubs. If you listen to the old Spanish dub of "Solid Serenade" for example, you will hear that the soundtrack is identical to the American one, the sound effects are the same. But if you listen to the recent dubbing (or anyway the recent dubbing of this short regardless), you will hear that the sound effects are different. Apparently, over the years they have remade some instrumental tracks (I don't know why), using music that apparently still exists, and adding new sound effects, especially from the Jones period. For "Trap Happy" instead, it seems that the instrumental track has not been used in the recent dubs, so I thought it didn't exist. But if you listen to the old Spanish dub you will hear it in Tom's scene at the phone. Another case is "Northwest Hounded Police" which uses only the music in the instrumental track, with no effects.
There would be many things to discover about the instrumental tracks of the MGM shorts, but in essence, they seem to exist, and so they could also exist for shorts like "The Yankee Doodle Mouse", but who knows where.