You're saying that shielding on the "inside" of the battery door (the part where one side faces the batteries and the other side faces the "outside air" around the scanner) helps reception?
I'm willing to give it a shot, especially considering I haven't been seeing the issues you have. It'll make for a good "control" or comparison.
The one time I do have demonstrable interference/attenuation is when the radio is plugged in to a USB power source while it's receiving. Similar to what you say with regards to the "hissing" - if I plug in the USB charging cable, a noticeable hiss/degradation in reception occurs, but only on a fairly narrow chunk of VHF in the 155 MHz range. All other bands appear unaffected.
Just out of curiosity, have you tried putting shielding on the "other side" of the batteries, i.e. in between the batteries and the SD card?