I am currently weighing up the advantages and disadvantages between DI and SL. However, I have found myself in the following catch 22 which implies that I should just use SL
My opinion is that it depends. Sometimes one is better and sometimes another. But I'd say that generaly I prefer DI. There are few reasons for that.
When dependency is injected somehow into component it can be treated as part of its interface. Thus its easier for component's user to supply this dependecies, cause they are visible. In case of injected SL or Static SL that dependencies are hidden and usage of component is a bit harder.
Injected dependecies are better for unit testing cause you can simply mock them. In case of SL you have to setup Locator + mock dependencies again. So it is more work.