The PMT lifespan issue isn't necessarily a problem, we have a 1970's scintillation counter that's been turned on for nearly its entire life and its just as good as it once was. The PMT really needs to be properly shielded from interference, they'll be the ambient static magnetic fields that'll affect the gain, but more importantly there's a lot of high impedance nodes they'll have as much of a problem, so in short you really need to keep it inside something like a paint tin with coax feed-throughs for your terminations. (as per the diyphysics link posted earlier)
The PMT will probably need to 'relax' for a while before any dark counts die down to their ideal values. As a rough guide a scintillation probe with a 2mm x 1 inch diameter sodium iodide crystal that i'm familiar with starts up counting about 10k counts before settling down to about 10 counts/second after a minute or so, and those are only the counts that come into the discriminator window.
If you need a sanity check on whether that noise is related to your dark counts, store the PMT in the fridge or freezer for a little while, and see if the noise changes characteristics at all.
A good trick for eliminating the dark counts is to use a coincidence counter. In its simplest form its basically an AND gate with fast monostables on the inputs, but that all depends whether you can couple two PMTs onto the scintillator.
Coupling to the scintillator is also a problem in its own right, you need very clean and polished surfaces and some optical coupling grease,