I was able to beat the Cthulhu campaign this weekend.  For those who are throwing their androids against the wall, I hope that this helps.

1/  Solo with Jenny.  Simple enough, she has a great ability and it makes it simpler to control.

2/  You should be able to get the 7 Elder signs in the Museum without any doom tokens.  If you have 1, don`t worry about it.

3/  When in the pacific, focus on the Relic items until getting the 3 gems.  Having the artifact which allows you to replace 3 green dice is also going to be extremely handy.  Use Excess investigation dice to get the 30 necessary tokens needed to find Ryleth. 

4/  VERY IMPORTANT, is to take your time.  I found that this scenario is kind of like Conflict at the Carrock for Lord of the Rings.  It looks really scary until you learn how to beat it.  I was using Jenny slowly to accumulate tons of Trophies.  I went to the hospital many times to ensure she was healthy.

5/  By the time the doom token was 10, I was spending lots of time in the ship stockpiling clues and spells.  I faced Ryleth with about 7 clues, 2 lock spells, and 1 relic to replace 3 green dice, all in addition to Jenny`s red and yellow dice.  Needless to say, the boss fight was pretty easy.

Good luck!