If the areal density increases uniformly in both directions, then you can expect that the read/write speed goes up by the square root of the areal density increase. That is, for 43.75 you'd expect a speed increase of at least between 6 and 7 times. Note that sometimes the density increase is achieved in only one direction or the other, depending on what technology was used to achieve it, in which case all or none of the density increase results in speed increase.
You can achieve speed increases by using multiple heads. LTO and the 3590/3592 proprietary tape technology on which it is based use 8 or 16 tracks read/written simultaneously, with tracks interleaved. There might be 256 tracks with tracks 1, 17, 33, ..., 241 being accessed, then 2, 18, ..., 242. etc. Doubling the number of tracks (density increase of 2 widthwise) wouldn't increase read/write speed. Doubling the number of tracks while simultaneously doubling the number of heads would.
Note that with 8 or 16 heads spread across the tape width, error correction is achieved by writing a matrix of bits (across the tape as well as down the length) with ECC bits added.