Hi Robert.
Sounds like you're having plenty of fun!
From my experience, there is only one thing that you can really do to establish if the changes are algorithmic or not and that is to benchmark your clients sites against their competitors.
If you know how very similar sites are being affected by an algorithm update you can always tell if it's just you or all the similar sites in your niche.
It's not enough to pick a few random sites in that are ranking in serous for your main target terms. You need to dig a little deeper than that.
Who are your clients real competitor. Consider their target audience (demographics as well as geographical locaton). What about the size of the business and their suspected online budget. What about the approach they'be taken on their site, blogging frequency etc?
You'll want to monitor the performance of sites/businesses that are very similar, somewhat similar and dissimilar but related.
It can be reassuring to a client to be told that even though there'should been a massive shake up in the serps - they are still out raking their competitors.
Another thing to consider is how an algorithm update might change the search terms that people use to find your clients.
If the serps are now being dominated by large players, does this mean there is a knock on effect as searchers start using more specific keywords to find the little guys/in dependants?
Or don't they give a stuff and are just happy to go with whoever appears at the top of the search results.
My tips:
Don't just rely on rank trackers - make sure you take screen shots or capture the serps so you can determine the winners and loses following an update. You can then use this info to find out where the top 10 sites are ranking following an update. (Hard to do if you'be not tracked who they are)
Keep an eye on webmaster tools and track the impressions as well as clicks. Impressions may show the impact of an algorithm change more obviously than rank tracking or looking at your organic search numbers.
Make sure you keep a fantastically good record of every change that happens to the site and make sure your client understands the need for a robust change control process.
When trying to determine if it's an algorithm change or just a cockpit ... I'd be more likely to put my money on "cockup".