What Akas refers to is using the Link2SD app, which is "kind of" App2SD, but much more flexible: You can get the entire app moved out (not just parts), and can even move apps you otherwise couldn't. But Akas missed one important part: your device must be rooted in order to use this special way.
As to the other part of your question: Sure you could uninstall the updates of Google Play Services -- but that wouldn't help you in any way, as the app will automatically update itself again. Furthermore, there might be dependencies, as other apps use this service (e.g. Google Play to access the playstore, and others). So newer versions of those apps might rely on newer versions of the Play Services.
Maybe someone digged (or will dig) a little deeper into all those dependencies and what can be done about them. It might end up in using some "legacy apps" -- like e.g. the Legacy Playstore (original post), while the original ones could be frozen/removed. Maybe all this is possible -- it again would require you to root your device, as these apps need to be installed as system apps.
While we all wish our devices might have a long life: if you look at the specs of your two-years-old, and compare it even with todays low-end devices, you will see the difference. And if you compare app sizes from two years ago ("What? 1 MB app size? Too big!") with todays ("Unfortunately, the play store has a limit of 50 MB app size, were we cannot fit our app into"; with my own words the summary of LibreOffice for Android), you see were it goes. And while I fully agree that core services/apps should be kept slim, there's nothing we can do about that...
Enough theory: if your device is rooted, or rooting it is acceptable (and doable) for you: Akas recommendation seems the best way out for you.