@Alan-Brand Well, I ran that command, but I'm not sure yet. I was initally getting out of memory errors, so I added a 256MB swap file, and then kept going, and now I'm getting a "IOError: [Errno 28] No space left on device"??? Hello... there's only 13.3G of free space on the micoSD? 
Edit: Monkey behind the keyboard then realises that he had stupidly and willfully skipped instructions from earlier, and said error message was a result of not enough space in /tmp. Error message could have pointed that out though!
Later Edit: I can now confirm that after a) adding some swap memory b) following the instructions properly and possibly c) doing the ln -s /usr/bin/gcc /usr/bin/ccache_cc suggested by @Alan-Brand that I have OctoPrint 1.3.1 installed and running. I see 1.3.2 is now out and about, but I haven't tried it out just yet. 
Even Later Edit: Ok, decided to download and roll out OctoPrint 1.3.2 since I'm fiddling around with stuff. Configured without a hickup, and is now running happily. Instead of the root user patch, you are better off using the bypass option that is present now in OctoPrint... so instead of adding octoprint & to /etc/rc.local you want to add octoprint serve --iknowwhatimdoing & The same would apply to 1.3.1, and as far back as whenever that option was introduced.
root@OctoPrint:~/OctoPrint-1.3.1# pip install -r requirements.txt
Processing /root/OctoPrint-1.3.1
Requirement already satisfied: flask<0.11,>=0.9 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Collecting Jinja2<2.9,>=2.8 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached Jinja2-2.8.1-py2.py3-none-any.whl
Requirement already satisfied: werkzeug<0.9,>=0.8.3 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Collecting tornado==4.0.2 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached tornado-4.0.2.tar.gz
Requirement already satisfied: sockjs-tornado<1.1,>=1.0.2 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-requirements.txt (line 10))
Requirement already satisfied: PyYAML<3.11,>=3.10 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Requirement already satisfied: Flask-Login<0.3,>=0.2.2 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Requirement already satisfied: Flask-Principal<0.4,>=0.3.5 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Collecting Flask-Babel<0.10,>=0.9 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached Flask-Babel-0.9.tar.gz
Collecting Flask-Assets<0.11,>=0.10 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached Flask-Assets-0.10.tar.gz
Collecting markdown<2.7,>=2.6.4 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached Markdown-2.6.8.tar.gz
Collecting pyserial<2.8,>=2.7 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached pyserial-2.7.tar.gz
Requirement already satisfied: netaddr<0.8,>=0.7.17 in /usr/lib/python2.7/site-packages (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Collecting watchdog<0.9,>=0.8.3 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached watchdog-0.8.3.tar.gz
Collecting sarge<0.2,>=0.1.4 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached sarge-0.1.4.tar.gz
Collecting netifaces<0.11,>=0.10 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached netifaces-0.10.5.tar.gz
Collecting pylru<1.1,>=1.0.9 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached pylru-1.0.9.tar.gz
Collecting rsa<3.3,>=3.2 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached rsa-3.2.3-py2.py3-none-any.whl
Collecting pkginfo<1.3,>=1.2.1 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached pkginfo-1.2.1.tar.gz
Collecting requests<2.8,>=2.7 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached requests-2.7.0-py2.py3-none-any.whl
Collecting semantic_version<2.5,>=2.4.2 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached semantic_version-2.4.2.tar.gz
Collecting psutil<3.3,>=3.2.1 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached psutil-3.2.2.tar.gz
Collecting Click<6.3,>=6.2 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached click-6.2-py2.py3-none-any.whl
Collecting awesome-slugify<1.7,>=1.6.5 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached awesome-slugify-1.6.5.tar.gz
Collecting feedparser<5.3,>=5.2.1 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached feedparser-5.2.1.zip
Collecting chainmap<1.1,>=1.0.2 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached chainmap-1.0.2-py2.py3-none-any.whl
Collecting future<0.16,>=0.15 (from OctoPrint==1.3.1->-r requirements.txt (line 10))
Using cached future-0.15.2.tar.gz
Exception:
Traceback (most recent call last):
File "/usr/lib/python2.7/site-packages/pip/basecommand.py", line 215, in main
status = self.run(options, args)
File "/usr/lib/python2.7/site-packages/pip/commands/install.py", line 324, in run
requirement_set.prepare_files(finder)
File "/usr/lib/python2.7/site-packages/pip/req/req_set.py", line 380, in prepare_files
ignore_dependencies=self.ignore_dependencies))
File "/usr/lib/python2.7/site-packages/pip/req/req_set.py", line 620, in _prepare_file
session=self.session, hashes=hashes)
File "/usr/lib/python2.7/site-packages/pip/download.py", line 821, in unpack_url
hashes=hashes
File "/usr/lib/python2.7/site-packages/pip/download.py", line 663, in unpack_http_url
unpack_file(from_path, location, content_type, link)
File "/usr/lib/python2.7/site-packages/pip/utils/__init__.py", line 605, in unpack_file
untar_file(filename, location)
File "/usr/lib/python2.7/site-packages/pip/utils/__init__.py", line 578, in untar_file
shutil.copyfileobj(fp, destfp)
File "/usr/lib/python2.7/shutil.py", line 52, in copyfileobj
IOError: [Errno 28] No space left on device
root@OctoPrint:~/OctoPrint-1.3.1# free
total used free shared buffers cached
Mem: 125748 35696 90052 7392 660 15984
-/+ buffers/cache: 19052 106696
Swap: 262140 15060 247080
root@OctoPrint:~/OctoPrint-1.3.1# df -h
Filesystem Size Used Available Use% Mounted on
/dev/root 5.5M 5.5M 0 100% /rom
tmpfs 61.4M 21.1M 40.3M 34% /tmp
/dev/mmcblk0p1 14.5G 510.7M 13.3G 4% /overlay
overlayfs:/overlay 14.5G 510.7M 13.3G 4% /
tmpfs 512.0K 0 512.0K 0% /dev
