Tiny leak in soldered copper 1/2" pipe joint
If you can drain the pipe (heating it with water in it is mostly an exercise in futility), then yes, you could try heating it and adding more solder in place. (Which, contrary to your assertion, is not an especially bad idea.)

If not, and you really don't have space to move things, usual practice would be to cut it out and install a "detour" loop -- two L's to bring it out of the plane of the existing pipe, two more L's with a piece of pipe between them to bridge the gap, and two more short pieces of pipe to connect the L's in the old pipe to L's in the new pipe. That gives you the play in the system that you need to bring things together, by letting you make the final connection at right angles to the old pipe. (Of course the downside of this approach is that you have to make eight good soldered connections, not just two, and it costs you a bit more for the extra pipe.)

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