Until recently, I've been using a pycnometer almost constantly all day. And yes they are simple, if tedious, to work with. However, if you're soppy, you won't get good results. There is simply no shortcut to the tedium.
A pycnometer must be scrupulously clean. My standard method was to soak it in hot soapy water, and rinse with distilled water thoroughly, before drying the cap, and pycnometer in a 105 C oven. The thermometer can't be treated that way (I absent-mindedly tried once, sent all the mercury to the end and it never left,) but still must be cleaned and dried. The assembly is never touched, not even with gloved hands, I carry it in a folded up kimwipe as a holder. For quarterly calibration, the empty dry pycnometer is weighed in triplicate. This is, in some ways not needed, the mass is never different, not even at the 4th decimal place. But at least it establishes that the balance is reliable.
Then there's triplicate runs of distilled water. This is where simple, but tedious comes in. You fill with water, you drop the thermometer in, some overflows, but you check the temperature. You warm in your hand until almost 25 C, using a kimwipe to soak up droplets as it overflows from warming. The last mounded droplet, on the pycnometer side-arm, at exactly 25 C is removed with the corner of a kimwipe. If you suck the water out to below the side arm's level by capillary action -- screw you, start over. If its OK, put the cap on, and read the mass. In triplicate.
Here's something I observed, that you don't hear about anywhere else. The first reading is often lower than subsequent readings. I don't know why that is, perhaps the ground glass joints hold water within them? Or maybe the glass itself has microscratches that make it porous. Anyway, I always fill, set it up and then dump the water out a few times before the first mass. And of course, you don't take any sample readings without a through rinse, especially when the sample is nothing like water, for example, a solution of an emulsified fat that's meant to add viscosity to a formulation.
Trizocy:, you seem to want really good results, but you don't mention how much work you're going through to insure your accuracy and precision. You keep telling us one number, on average, but how close are your numbers to each other? How close are they to the theoretical density of water at room temperature?
P.S. of course, I neglect to mention, I also have to calibrate my pycnometer fitting thermometer to a NIST standardized thermometer. That's a little too much to expect of you Trizocy:. However, bear in mind that in my experience they always deviate -- at least by 0.5 C, sometimes as much as ±1 or 1.5 C. You can certainly check at two points -- 0 C for ice and water, and 100 C for boiling water. If the thermometer can handle boiling temps (c.f. above.)
*EDIT -- I spell better later in the day*