The difference using some of the shielding material should be noticeable - people have used “audiophile” RFI absorbers and noticed the results. In general the biggest digital offenders are the biggest chips 
I don’t want to take the time to wade thru all of the options and make specific recommendations, but here are the best places to try and the frequency ranges of interest:
In Sr: The PIC/control processor/display processor on the back of the display board is the worst offender in the box. (80MHz plus all sort of impulses reading flash and ram, etc.) In the Jr the control processor is the one that says “PIC 32”.
Probably 2nd most offender is the Bridge (high clock rate - 100s of MHz and lots of current.) It’s the chip on the little daughter card on the Bridge II or on the little daughter card in the Jr next to the Ethernet connector.)
I don’t know which of the following causes the least or most RFI/EMI:
The USB processor is next to the USB connector, a little smaller and says XMOS. (About 400MHz + harmonics)
In the Jr the Ethernet PHY is near the network connector and says “ASIX” About 125MHz and probably not the worst offender.
The FPGA says “Spartan 6”. (some 22.6MHz, a little less 56MHz and a lot of 170MH - the number vary a little from release to release.)
The two small inductors near the USB chip might be a place to try if you can make sure that nothing can get shorted - they are part of the XMOS chip’s power supply so they have a lot of changing current.
In the DS Sr if your digital board still has rectangular epoxy PCB material just over where the audio transformers are, adding some magnetic shielding to the BACK of the digital board might be useful. Make sure to not short anything. There are no traces in those rectangle on any lower of the board.
There’s probably no reason to shield any of the other bigger chips (mostly regulators and higher current diodes.) But it shouldn’t hurt.
On the analog board there are only two places I’d try anything, both just under the ribbon cable: the oscillator module (22.6MHz) and the big 28 pin digital switch (which says “MC100E…FNG” - 11.3MHz.) Some people have reported good things when shielding them and others the opposite.
You might also find that wrapping some of the absorbing material around your power cord and/or you interconnects (especially digital interconnects) may make a noticeable difference, perhaps good, perhaps bad depending on the rest of your system.