Re: vhf interference
Couple of things here to add to Bruce's excellent suggestions.
You changed two things and this problem occurred. With that said, you don't know which is the culprit.
There are two types of emissions: conducted and radiated.
Conducted emissions come through the power lines and radiated come into the "front end" of your receiver, either via the antenna, or by some unshielded circuit receptive to the signal or one of it's harmonics. The closer to the antenna the easier to have them interfere, but the frequency is higher there which also makes it harder for interference to bother you.
VHF antennas are tuned to VHF frequencies which are in the 100's of MHz whereas your depth finder operates at 200 kHz.......1000:1 difference. I don't see how the internal electronics of your sounder can be at fault as these are millivolt signals and have to have a way to get out so that your antenna can pick them up. It is possible that you are getting some radiation from the cable that goes to the transducer from the Eagle since you have 200 kHz electromagnetic waves present there which are converted to acostic waves by the transducer.
Don't know the bandwidth of your antenna, but the front ends of radio's can pick up microvolts (10 exp-6 volts) which is not very large. Moving your antenna 30 ft away may not be far enough for a valid test.
If Shakespeare is recommending a different antenna, maybe the bandwidth is tighter which would reduce the signal level of spurious from the Eagle.
In addition to Bruces testing you might put shunt capacitors across the power lines in addition to twisting them together (that he recommended) at about 1-5 turns per inch. A "Ceramic Disc Capacitor" of 1 microfarad, 50 DCWV (from Radio Shack) would be a good choice if the 200 KHz is your culprit. That should be large enough for that low a frequency yet low loss enough to function properly. The leads need to be as short as possible and as close to the units as possible. You can stabilize the body of the disc (from vibration) with RTV stuck to whatever is handy.
The last thing is a "single point" ground/power source (like Burce suggested). Since your radio and Eagle have internal power on-off switches this is easily accomplished. The battery terminals are the source of your power and should be the origin for these two sets of power lines. Single point means that everything that gets power gets it returned in parallel to the power source, especially grounds, rather than in series (daisy chain). A daisy chain adds all the ground currents of all the equipment connected together and sensitive front ends of receivers can pick up this "noise"; power line too but ground is the worse.
Last is is possible to put your original antenna back on for testing purposes. This would at least tell you if your antenna, or rewiring is the culprit.
Mark