Alternative ways to maintain temperature stability of silicon BJT circuits other than feedback resistors
You have a number of misconceptions.  Your basic understanding of how a emitter resistor provides negative feedback and thereby stability is correct, but some of the so-called "rules" you quote are just silly beliefs.

I can't even guess what archaic religious ritual derived the value of 1.4 V for being across the emitter resistor.  That's just nonsense.

The base-emitter junction looks like a diode to the circuit driving it.  As with regular diodes, a small change in voltage can cause a large change in current.  Or conversely, the diode voltage varies little over a large change in current.  Therefore, even a little voltage change on the emitter can make a big difference to the base and therefore collector currents of a transistor when the base voltage is being held fixed.  The emitter resistor value in this usage is a tradeoff between generating enough voltage to provide meaningful feedback, but dropping little voltage to not get in the way of the intended operation of the circuit and to not dissipate significant power.

For example, the final output stage of a audio amplifier that drives a 8 &Omega; speaker might only use 1 &Omega; or maybe even just 100 m&Omega; emitter resistors.  At 1 A, even the 100 m&Omega; emitter resistor will cause a 100 mV offset in the base drive.  100 mV across the B-E junction can make a large difference in base and collector current.

The diodes you show in series with the emitter actually make things worse.  Remember that the voltage across a diode changes little with the current thru it.  That's opposite of what you want.  As the current thru the resistor gets too large, you want whatever is in series with the emitter to drop more voltage, thereby decreasing the B-E voltage.

Another problem with diodes is that the voltage across them at the same current goes down with temperature.  This is also backwards of what you want.  As the current gets higher, the diodes will dissipate more power, and decrease their voltage in response.  This causes more current, which makes them hotter, which causes even more current, etc.  This is called thermal runaway, and is a issue you have to consider when designing BJT circuits that handle significant power.  Note that the B-E junction has the same temperature characteristics, so a BJT can have thermal runaway on its own, even without this being helped along by additional diodes in series with the emitter.

It can be useful to use diodes in the base drive part of the circuit to compensate for the B-E voltage of the transistor.  That, together with a properly chosen emitter resistor can be a useful way to bias a BJT.