Yes you could make such a system work BUT and it is a very big but you need to source some non stretching magnetic tape and to accurately mark the tape with the reference signal or signals for a quadrature or coded position signal. The tape use for audio recordings stretches under modest tension. In the early days of magnetic recording fine iron wire was used but this will mean building special recording heads as the magnetic flux will be many time higher than that required for modern audio tape. The poor high frequency response of the wire recording will limit the accuracy obtainable as will your ability to lay down an accurate reference track.
Sorry but suggest you use optical sensors.
Regards
Pat