Sorry to appear so dumb with a problem I am sure is not unique.
I want to mount LEDs a few feet from the PC board or whatever device to which the LED is anchored.
I have searched the internet in vain to find either LEDs with such longer, flexible leads, or suitable sockets in which to mount an LED.
I blew a couple of bulbs by trying to solder wires onto the leads.
Is there a source for the ready-made LED I seek?
Should I learn how to prevent blowing a light with more cautious soldering technique?
Should I find another hobby?
You might want to look at two pin DuPont header connectors and plug your LEDs into them:
Header connectors
Improving your soldering technique/equipment is a great option.
You can make leads as long as you want if you know how to solder. Heat shrink it if you're feeling adventurous (or liquid electrical tape or tape tape, whatever works for you)
You obviously should not be killing LEDs while simply soldering wires to leads. Get a helping hands device, set it up how it ought to be. Make sure your soldering iron is hot enough. A lot of newbies use insufficient irons with tougher to melt lead-free solder and end up holding the iron on components far too long and killing them.
INTP:
Get a helping hands device
Mine is called Blu-Tack. 
Soldering is about having the right temperature, pre-tinning all the components, and working fast.
If it doesn't work the first time, let the work cool right down before trying again - much less heat
damage that way. LEDs are more heat sensitive than most components because they are made
from a low-melting point plastic without glass-dust filler (most electronic components that look
plastic are glass-filled epoxy, which keeps it shape when heated close to the melting point).
Cool the component immediately after soldering and you 1/2 the heat transfer.
I've actually made use of a small copper alligator clip to act as a heatsink to buy myself a little insurance when soldering LEDs to wire.
I also found Dupont connectors and have never looked back, especially considering there's multiple outlets to purchase pre-crimped terminals on wire (multiple colors and lengths.)