How can I 'stretch' a signal in time using analog components?
There IS one analog technology that can be used to do the job ... the CCD "bucket brigade" delay line.

It IS analog, but it has a lot in common with digital techniques in that it's a sampled-data system. 

A typical CCD delay line has 512 or 1024 capacitors in a line, and a network of CMOS switches to interconnect them. It works roughly as follows:


Charge one capacitor up to the voltage on the input pin, 
Hold that voltage, and charge the second capacitor up to the first one's voltage, 
Hold that voltage, and charge the Cap 3 from Cap 2 while charging Cap 1 from the input pin.
Repeat, charging even from odd, and odd from even, until the first sample appears on the output pin.


The general idea is like a line of people passing buckets to one another, to try to fight a fire.

At this point, if you want to change the pitch, you need to store new data into a second CCD at the input sample rate, while you empty the first one at the new sample rate (in your case, half the original clock rate).

As the second CCD is full while the first is only half empty, you now have a problem : you have to dump some of the data. If you have more than 2 CCD delay lines you can "conceal" the joins by cross-fading from one to the other, while filling up a third, but it isn't a perfect technique.

CCDs have pretty poor noise and distortion specs, along with all the spectral and aliasing problems of digital audio, so you won't hear much about them this side of 1980.

One such example is the SAD1024 (datasheet here) used as a pitch shifter (with continually varying pitch, aka a flanger) here