I'd remove the spring antenna by desoldering if possible. Just in case you might want to revert to it. If you leave it in it does add some inductance which would change the tuning of the antenna.... basically making things theoretically more complicated, but it might still work well enough.
You might try to find a thinner coax cable, otherwise you could try bringing a short wire for the antenna and another for a ground out of the case, then soldering those to the coax. If you don't care about keeping the coiled antenna, you might straighten it out, run it outside the case and then clip it short before attaching it to the coax. You'd still need a ground wire for the outer conductor of the coax, though.
Basically what you're trying to do is use the coax as a transmission line that gets the signal through the metal wall. Once the coax is out of the wall, stripping off the outer conductor leaves the inner conductor to work as an antenna.
The "resistance" mentioned is actually called "impedance" as the signal is AC. Impedance takes into account the added complexity of alternating current running inductive (like the coiled antenna) and capacitive elements. In a perfect world, we would want the impedance of the antenna and transmission line to match that of the transmitter. This allows for maximum power transfer. The worse the match, the more power is wasted. We're just sort of winging it here hoping the power loss won't be bad enough to matter.
It's the same concept as matching your stereo speakers (usually 4 or 8 ohm impedance) to your amplifier to get the best performance.
You might try to find a thinner coax cable, otherwise you could try bringing a short wire for the antenna and another for a ground out of the case, then soldering those to the coax. If you don't care about keeping the coiled antenna, you might straighten it out, run it outside the case and then clip it short before attaching it to the coax. You'd still need a ground wire for the outer conductor of the coax, though.
Basically what you're trying to do is use the coax as a transmission line that gets the signal through the metal wall. Once the coax is out of the wall, stripping off the outer conductor leaves the inner conductor to work as an antenna.
The "resistance" mentioned is actually called "impedance" as the signal is AC. Impedance takes into account the added complexity of alternating current running inductive (like the coiled antenna) and capacitive elements. In a perfect world, we would want the impedance of the antenna and transmission line to match that of the transmitter. This allows for maximum power transfer. The worse the match, the more power is wasted. We're just sort of winging it here hoping the power loss won't be bad enough to matter.
It's the same concept as matching your stereo speakers (usually 4 or 8 ohm impedance) to your amplifier to get the best performance.