Using a coax loss calculator (something that everyone with questions like yours should have) I come up with the following values:
RG-6 loss @ 160 MHz for 80' of coax - 2.864 dB
LMR-400 loss using the same factors - 1.255 dB
Link to what I used so you can play around to find the best solution for you.
Coax Calculator
Since lower loss is generally better, changing the feed to LMR-400 may help. Will the 1.6 dB matter? Who knows, it may and it may not. That's not a great deal but could be enough to matter.
There are several other things that may be going on. All could be causing your problem but there's no guarantee than any of them are.
1. Is your antenna pointed in the right direction? A yagi is very directional so being off even a few degrees may be the difference between a fully quiet signal and one that's very noisy. Try rotating it to see if you can get better signal strength. Remember that just because the agency is in one direction, their transmitter may not be there, especially if there are mountains in the area.
2. Do you have any large obstructions (tall buildings, hills, mountains, etc.) between you and what you want to listen to? They could be blocking the signal.
3. Do you have strong stations nearby or in line with your antenna's main lobe? They could be overloading your receiver and causing it to become "deaf". It could be powerful paging transmitters, NOAA Weather Radio transmitters, FM or TV broadcast stations or even some 2 way radio transmitters.
4. Is your current coax in good condition? It could be damaged by water, which will ruin its ability to pass signals well. It may be due to improperly installed (or incorrect types) of connectors, connections not sealed against water, cracks or other breaks in the coax's outer plastic covering, etc.
5. Is your antenna designed to work on the frequency range you're trying to pick up? One designed for UHF may not work well on VHF for example.