No counters, but other digital chips are allowed...seems odd.

The 555-4017 circuit I had in mind could be set up to start at one of the dead time periods them move on to the first fan time period.

So, the sequence would be something like:

Power up
Maybe a 4 second delay (a guess)
70 second fan time
3 second dead time
70 second fan time
3 second dead time
etc...

 

NOTE:

You can reduce the start/run time differential of a 555 by augmenting the control voltage.

 

NOTE:

You can reduce the start/run time differential of a 555 by augmenting the control voltage.

That's true but would need to be augmented only once.
Right off hand seems it might be more involved then using the resistor divider

 

No, it's just a single resistor from CV to the negative rail.

You simply lower both thresholds and the timer works just the same as always.

 

No, it's just a single resistor from CV to the negative rail.
You simply lower both thresholds and the timer works just the same as always.

But it's that first charge period that throws the timing off as the timing capacitor must initially charge from 0 to 2/3 Vcc.
After which it charges between 1/3 and 2/3 Vcc.
It's not really a big deal unless the timing cycle is very long.
Another alternative as you suggested using the CV pin 5 is connecting a schottky diode that is activated when the output is low.
With this configuration the cap charges to 2/3 Vcc but now must discharge to appx 0.1 volt before switching.