So I'm planning on going away for grad school in a year or so, which means I'll probably be in a smallish apartment, where I can no longer crank the Blues Jr. to my heart's content.

My playing of late involves a pedalboard that I've lovingly assembled over the past year, and lots of looping. I don't imagine that will be very satisfying to play with the volume down at 1.5. How can I get a better sound at neighbor friendly volumes? I've heard pignose amps (e.g., the 7-100) handle pedals pretty well, but I haven't seen anyone using anything more intense than a boost pedal on one. Another option might be an attenuator. Possibly this one, which seems to have been made with Fender amps in mind.

How do those options sound? And how well might they work with an occasionally very fuzzy pedalboard?
The only options that I can think of is either an attenuator, or possibly, if you have some sorts of recording interface, and mic, build an iso-box, and just jam through some headphones.

Unless you have some recording gear already, your cheapest option would be an attenuator.
PRS Custom 24
Gibson Les Paul 60's Tribute
85' MIJ Strat
97' Snakepit Les Paul
LP Traditional 1960 Zebra
MIJ Tele
MIA Strat

Silver Jubilee 2525
Peavey Ultra 112
Jet City JCA50H
66' Bassman
Pink Paisley Princeton RV
74' Vibro Champ
Isobox is interesting, maybe a bit bulky and involved for my purposes.

Anyone know of any good attenuators for a Blues Jr., if that's the only other option?
Don’t waste money on an amp for low volumes. Almost none of the amps made for low volumes actually sound good at low volumes, and almost no guitar speakers sound good at low volumes, so if you want to use a small amp quietly you’ll need to drop more money on a high end 8" or 10" speaker.

Instead get a preamp pedal with a built-in speaker simulation and plug it into a set of small studio monitors, either M-Audio or one of Behringer’s Roland clones. All the Blackstar HT distortion pedals are preamps, so are the Tech 21 amp emulation pedals. Joyo makes clones of the Tech 21 pedals (~$35 on eBay) that don’t allow disabling the speaker emulation, but in your case that’s not really a drawback.
Tech 21 Blonde Pedal+Mini sound board or Rolls/Behringer headphone amp+headphones. Alternatively, get a Zoom G3, set it at the end of your chain on a Fender amp model setting, and plug your headphones in. This will sound better than any magic you can work with your current amp.
Telecasters-->Dunlop Volume Pedal-T1M Pearl-AMT Japanese Girl Wah-Line 6 M9-Ibanez DE7-EHX Cathedral-->Mesa Boogie Nomad 4x10 combo
I play through a 4 Track Cassette Recorder myself in my room. Very quiet, and I can record demos and whatnot.
Put a $40 Behringer Ultra-G 4x12 cab sim on the output of the pedalboard and plug it into your stereo. It sounds great.
Hmm interesting... Will I really be able to get a better low-volume sound from the speakers I'm using for my computer than I would from my amp + attenuator? If so that would definitely be an intriguing way to go.