The first big room has no Unowns, the second has “F”, third has “R”, forth has “I”, fifth has “E”, sixth has “N”, and seventh has “D”. Needless to say, these particular letters will be the easiest to find. The dead-ends contain the rest of the alphabet. Check each individual dead-end four times each to quickly catch as many letters as possible.
Once the tunnel is finished, it should connect to the ruins.