If logread -t adds a [123456789.123] additional epoch second timestamp after the ctime() one as its code suggests, you should be able to do it with just busybox awk:
logread -t | awk ' BEGIN {lastminute = srand(srand()) - 60} match($0, /\[[0-9.]+\]/) && substr($0, RSTART+1, RLENGTH-2) > lastminute { print substr($0, 1, RSTART - 32) substr($0, RSTART+RLENGTH) }' srand(seed) seeds the PRNG and returns the previous seed. When not passed a seed, it uses the current epoch seconds, so srand(srand()) returns the current epoch seconds.
Then we look for [digits-and-dots], remove it and print if digits-and-dots extracted from it are after lastminute.