I have had problems sourcing springs myself for a different instrument than yours but I managed to find some decent new ones pretty easy.
These are the options you have
1 Shop around for a supplier of the correct spring
2 Measure the diameter and the length of the existing spring when it is removed from the instrument.
Then check out all the springs from an online music store for any brass instrument that is close to the measurements of your spring. They usually quote diameter and length at ordering time.
I found a tenor horn spring that matched the diameter and length of my trumpet spring and it worked just fine.
Downside is you wont know if it is suitable until you try on the other hand you only stand to lose a couple of quid and sometimes they are sold singly so you can buy one and see if it works then buy the other two.
3 The third option is to have a tech wind you a set, they can do this with bronze wire and they usually work fine.
On annealing
Spring steel is capable of hardening and this affects the strength of the spring.
A softer temper gives a gentle spring a hard temper gives a strong spring.
Heating a spring to cherry red then quenching fixes a very hard temper then heating the spring and then cooling it fixes a softer temper.
When making springs it is usual to make the spring fully hard and then temper it in a separate process, tempering really means softening by a known and predictable amount
The temperature you heat it to after hardening it can control the strength of the temper.
If you clean the spring so it is shiny and bright then heat the spring and observe the oxide that forms on the surface then quench the spring when the oxide colour is what you want following this table
Dark yellow 240 degrees (hardest)
Yellow Brown 250 degrees
red brown 260 degees
purple 270 degrees (softest)
If you keep heating beyond the purple oxide the steel begins to glow. These are the temperatures when you see glowing steel
very dark red 1100 degrees
dark red 1300
cherry red 1400
Much beyond that the steel glows yellow and then melts that happens around 1400 to 1500
As you can see the temperatures of correctly tempering steel are way below the melting point of steel, and we cannot use the colour of hot steel as that is way too high so we use the colour of oxides that form on the surface.
I would imagine the target oxide colour would be yellow brown as that would remove some of the hardness in the spring but would not soften it fully.
Remember this if you get it wrong it does not matter as you can reharden the spring many times without any problem, simply heat to cherry then quench in water to bring up the hardness to maximum and then go through the heat to dark yellow and quench or heat to yellow brown and quench or heat to red brown and quench.
You are in full control
All the heating and quenching does is excite the atoms and then fix them in a new arrangement that relates to hardness.
I have to say that this applies to steel springs which are the most common springs in use as far as I am aware.
This procedure cannot be applied to bronze springs. bronze melts at much lower temperatures around 900 degrees
Annealing of brasses and bronzes is nonetheless similar to steel.
Strictly speaking hardening and tempering applies to steel and annealing applies to softer metals that work harden, heating the softer metal relieves the stresses that lead to fracturing during and after work hardening, but the two terms are often used interchangeably these days.
