I read a book about how the Engima messages were decrypted by the British during the war. The 'Bombe' could decrypt three rotor messages in a few hours and had a processing speed of less than a thousand IPS. A modern computer should make the process trivial even for a six rotor Enigma, if one existed.

Why does problem being solved here require so much computing?

The bombe worked in a totally different way to the current mechanism. Essentially, the Enigma system is still pretty good. Part of the problem with this message could be a transcription error. If there are too many, we'll be trying to decrypt something that was different from the message that was sent, if that makes sense. I don't know enough to explain, maybe someone else does.

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The bombe uses completely different algorithm, for it to work, you have to know what may be there in the message and provide input data. Without it, bombe is useless.
The hillclimb algorithm uses dictionary based attacks, try searching 'hillclimbing enigma', I think you'll find an e-book/article which explains the mechanics nicely.

The next app I'm going to release sooner or later is going to be 'distributed bombe', since there are many machines attached it will be possible to attack the text(s) without knowing what's there just by using random cribs.
The problem is that the server environment for this type of attack is going to be very complicated, just thinking about this gives me headaches. I have parts of it already finished.
The worst problem is the bombe output, I have to find a way to use it to decode the rest of the message.

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M4 Project homepage
M4 Project wiki

I get it now. The Bombe used a known message to crack the daily rotor settings and took advantage of the plug board canceling itself out when doing so. You are trying the type of attack which the Germans new to be impossible at the time.

One question. Why is a four rotor Enigma several hundred times more complex than a three rotor Enigma? Should it not be 26 times more complex?

Because you have to check all Navy "Reflector/Greek" combinations in addition to the three rotors combination (3 of 8). The Army Enigma only used 3 of 5 without a Greek rotor...

Navy Reflector/Greek:

BB
BC
CB
CC

TBREAKER

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-=> Breaking German Navy Ciphers - The U534 Enigma messages <=-