So these may or may not be "worth it", but for free, it seems like the effort could potentially pay off. Though, if you had to pay for the VPSs, there's no possible way I can find to make a profit like this.

Sign up for Free VPS trials

Google and Microsoft both offer a couple hundred dollars to try out their cloud computing services. They're both a little bit complicated to figure out if you have never done something like that before, but with both of them you're looking for the pages that let you create VM instances. I used Ubuntu 16.0.4 for all of them. For the google ones, I used the 2 core option and made 6 of them. For azure I used one of the 4 cores.

Google - https://console.cloud.google.com
(Crucial note: the Google TOS specifically prohibit mining on the free trial. However, as far as I know, you can upgrade to the full account, set a budget to equal the free credits you were given, and just shut 'er down when you reach budget.)

Microsoft - https://portal.azure.com

Install the mining software

I've specifically been trying to mine XMR, so I had to find a miner that would be compatible. Of all the ones I tried, this one was the easiest to get working on the VPS. With Azure, I had to ssh in to get a command line for the VM. Google lets you open a terminal for each in a new window, which is really convenient.

sudo apt-get update

sudo apt-get install automake autoconf pkg-config libcurl4-openssl-dev libjansson-dev libssl-dev libgmp-dev make g++

sudo apt-get update

git clone https://github.com/tpruvot/cpuminer-multi

cd cpuminer-multi

./build.sh

./autogen.sh

./configure CFLAGS="-march=native" --with-crypto --with-curl

./cpuminer -a [algorithm] -o stratum+tcp://[pool address]:[port] -u [wallet address] -p x

Just plug in your info to the brackets on the last line and get to mining!

Use VPS to mine to Eobot

If you don't care to mine XMR, or don't want to mess with pools and all that, you can easily send the hashpower to eobot by changing the final command line to something more closely resembling this:

./cpuminer -a x11 -o stratum+tcp://x11.eobot.com:5555 -u eobot.[account number] -p x

It seems as if x11 is the most profitable option, but I only tried that and scrypt, and I got the feeling the VMs could actually find some shares with x11 and not so much with scrypt, but it was a pretty minimal test.

Personally, I kind of find eobot to be an unwise investment, but maybe someone can make it work. Either way, all these free accounts combined and sent to an eobot account mining GHS4 will end up netting you some free 5yr mining power, but I think it might be more worthwhile to go for bytecoin and sell it on exchange or Monero and hold in a wallet for a while.

Please let me know if you have questions or found this helpful.

I appreciate all upvotes, shares, and tokens of gratitude.

Have fun tinkering!