I work for a calibration company testing electronic instruments to prove they are accurate. One of the jobs that I do is to test crimp samples. I do a voltage drop test between the crimp and the wire, and follow that with a pull off test that checks the amount of force required to separate the crimp from the wire. If the crimp it tight enough I only see a very small voltage drop, if the crimp it too loose I see a larger volt drop. I can tell if a sample is going to fail the secondary pull off test by the results of the initial voltage drop test.
A loose or poor connection will generate heat as you get a certain amount of arcing between the two surfaces of the connection. A soldered joint makes sure there is no gap between the two connections and will stop the arcing. It looks like there are minor differences between the springs in terms of how tight the connection is between the spring and the mounting plate, at high current levels the amount of arcing will increase and generate more heat causing the spring to sag.
I would also add that it is possible that the 0.3 ohm coil that you have built may actually be of lower resistance than you think. Because of my job I have access to some high end test equipment used for measuring very low resistances. I know that it is accurate because it is calibrated to a traceable standard at the national physics lab. I had one of the cheap ohm readers commonly used, and the difference between my calibrated standard and the cheap ohm reader was significant.
A small decrease in resistance at this level will significantly increase the current passing through the spring causing the spring itself to heat up (just like your coil) and collapse.
What I am trying to say is you may actually be closer to the limit than you think. The spring sagging is a warning that something may be wrong. It might be your build at fault rather than the spring. Not because you have intentionally built too low but that the equipment used is giving false readings.
Good quality test equipment will have listed specifications in terms of accuracy. This is usually given in terms of a percentage of the reading or a percentage of scale of measurement. If you do not have this information the equipment should really be viewed as an indication only, in other words its roughly this. In general a good quality ohm reader that you can trust is going to run you hundreds of dollars not tens of dollars.