I think your best bet would probably be resistance soldering, and not flame.
Resistance soldering is often a tweezer/tong like tool that creates heat at
the contact points well, between them, actually, using the contacts to
create a path for the low voltage current.
With the RS method, the heat is generated within the workpiece itself, not
transferred or conducted into the workpiece from a source, such as torch or
electrically heated tip.
This has been the preferred method of assembling mulit-conductor connectors
with many solder connections.. such as military and aircraft avionics
You would need to practice with some pieces of the same size to find the
best heat range to attain full solder penetration of the joint, but the RS
method would accomplish the job with the least amount of damage to the
nearby composite material.
American Beauty is one maker, but there have been numerous others, and maybe
there still are a few.
A little added margin of protection could be had by using a cooling material
on the composite material, such as heat barrier foam or putty which could
easily be removed.
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