Just figured that I should update this question - it took a while to sort out all the details, but I got compiz working very nicely on Loki.

Here is my system:

                                     user@spinach
         eeeeeeeeeeeeeeeee           OS: elementary OS 0.4.1 loki
      eeeeeeeeeeeeeeeeeeeeeee        Kernel: x86_64 Linux 4.13.0-26-generic
    eeeee  eeeeeeeeeeee   eeeee      Uptime: 1h 2m
  eeee   eeeee       eee     eeee    Packages: 2167
 eeee   eeee          eee     eeee   Shell: bash 4.3.48
eee    eee            eee       eee  Resolution: 3840x1080
eee   eee            eee        eee  WM: Compiz
ee    eee           eeee       eeee  WM Theme: elementary
ee    eee         eeeee      eeeeee  CPU: Intel Core i7-6700K CPU @ 4.2GHz
ee    eee       eeeee      eeeee ee  GPU: GeForce GTX 1050 Ti
eee   eeee   eeeeee      eeeee  eee  RAM: 1968MiB / 32128MiB
eee    eeeeeeeeee     eeeeee    eee 
 eeeeeeeeeeeeeeeeeeeeeeee    eeeee  
  eeeeeeee eeeeeeeeeeee      eeee   
    eeeee                 eeeee     
      eeeeeee         eeeeeee       
         eeeeeeeeeeeeeeeee          

It was fairly straightforward for the most part.. but there were a couple of finicky things.

1. Install compizconfig settings manager AND compiz fusion icon from the appcenter.

• Compiz fusion icon is deprecated and doesn't do what it's supposed to do, but it does something (didn't take the time to figure out what) that makes everything work correctly. No idea why this is the case - maybe someone else can shed some light on it

2. Use killall wingpanel; sleep .3; nohup wingpanel & sleep .3; nohup wingpanel --toggle-indicator app-launcher as a command to get to elementary's app launcher

• Getting this launcher to work was quite tricky.
• It has to be restarted every time it is launched from the terminal (in compiz, not in gala). It's pretty buggy but eventually I figured out a workaround
• You may need to change the sleep times on your machine. Make sure that wingpanel has time to fully draw itself before trying to toggle the app-launcher

3. The notification-daemon must be manually started. This is probably easiest to do with an alias when you first start compiz.

Put this in your .bashrc to fix the notification-daemon:

alias co='nohup compiz --replace & sleep 2; /usr/lib/notification-daemon/notification-daemon;

And to get back to gala:

alias ga='nohup gala --replace &'

Now you can use 'co' to switch to compiz, and 'ga' to get back to gala - let me know if you would like my compizconfig file!