Well, not really, as far as I’m concerned, though it’s true that the Japanese R is quite unique, even if it’s supposed to be the same sound as the tapped R in Spanish (or at least, that’s one way of pronouncing it)…
Based on this, perhaps what’s happening is that you’re unconsciously trying to reduce or rush the second syllable, possibly because it uses the same vowel as the final syllable, or because you’re telling yourself that R and D are similar in Japanese, which is messing with your pronunciation. The very first time you say ‘karada’ in the recording, we can hear all three syllables distinctly, but once you start speeding up, the second syllable disappears. I suspect that what you’re doing is that you’re trying too hard to curl your tongue up for the R, and so it somehow gets ‘stuck’ in that position. Perhaps the ways you pronounce R and D in Japanese are too similar. I’m not sure.
In any case, for me, the main difference between R and D in Japanese is that for R, my tongue is further back in my mouth, pressing on the bump behind my teeth. (By the way, I don’t curl my tongue very much for the Japanese R. It’s more like my tongue is forming a little S in my mouth. The upper side of my tongue presses against the roof of my mouth, not the underside.) For D, my tongue gets really close to my teeth. Also, the R is a very light sound, simply requiring me to move the tip of my tongue downwards almost vertically, whereas for D, more of my tongue is pressed against the area behind my teeth, and it stays horizontal as it comes down. I also tend to release air with slightly more force when pronouncing a D instead of an R.
Something else that might help you (which will also give you the correct pitch accent, by the way) is focusing on pronouncing ら and だ at exactly the same pitch and for exactly the same amount of time. Go syllable by syllable. The way you’re pronouncing からだ now is more like ka-RA-Da. (Musically, in solfege using English-speaking musical conventions, it’s do-mi-re, or G-B-A if I’m not wrong about the notes – I needed a keyboard to compare the pitches, but I’m pretty sure about the intervals.) You start low, go high (up two tones), and then come down a little (down a tone). It should be more like ka-RA-DA: start low, go up about a third (1.5 tones), and stay there. Here are some samples: 身体 （からだ） の発音： 身体 （からだ） の 日本語 の発音 You need to allow yourself to complete the second syllable before moving on to the third. Make sure your tongue is fully disengaged from the roof of your mouth before you start forming the D. When you eventually start speeding up, you should feel your tongue lightly tapping/jabbing the roof of your mouth twice in a row, moving slightly further forward for the second tap compared to the first.