A company in California called Video Optics makes (or used to make) a solid state tube base. It does not use a typical resistor string in the voltage divider and provides a stable source of power to the PMT with low power usage. It runs off a single 9V battery. An external power supply or second cable is not needed, although it can be powered from a low voltage charger. It is a superior product that yields a spectrum which is far more stable than from a conventional tube base.
If you must use a standard voltage divider, then I recommend a strong and stable power supply with a 10 mA output. The power supply should be warmed up prior to first use (some manufactures specify 1/2 hour).
As John Andrews suggested, thermal insulation around the crystal and PMT will help.
All statements are my own opinions and not a product endorsement by my employer or clients.