Both digital and traditional balance beam reloading scales can be accurate, with some brands admittedly getting better reviews than others. Digital scales are, all things being equal, clearly easier to use but balance beam scales were the only game in town for many years and continue to be used, even preferred, by many reloaders.
First, there is no relation whatsoever between the type of press you are using and the scale you use. A scale that is accurate and reliable is suitable for use with any press; one that is not is suitable for no press.
Although possible (I suppose), it's highly unlikely that a scale could malfunction or drift off zero to the point where you could get a double load without noticing - double loads occur from poor reloading technique or inattention, not from malfunctioning scales. A malfunctioning scale could, however, result in an unsafe load. There are two things you can do with your setup to avoid that happening:
1. Get or make one or more check weights to verify the accuracy of your scale and then use them from time to time before, during, and after a reloading session. Check weights can be purchased for relatively short money or, if you have access to a scale of known accuracy, you can make your own by (for example) cutting short lengths of wire and noting their weight on the accurate scale (and then labeling them so you'll know what they are when you need them). Having satisfied yourself that your scale is accurate, you can then use it periodically - your idea about checking every 10th charge is a fairly common practice - to ensure that your charges are accurate.
2. Know what the correct charge of powder looks like in the cases you are reloading, in terms of how much it fills the case, and then look in each and every case to verify the charge before you seat the bullet. Get a flashlight and use it if you have to. That's something like what you're suggesting to do using the Lee measuring spoon(s), but it's more direct and you can, and should, do it for every round.
Edited to add: I see you added the part about the 10-10 while I was typing. The RCBS 10-10 is pretty much the standard of the industry in terms of balance beam scales and it will serve you well. Knowing you have a good scale, however, doesn't change anything I recommended about making sure it's accurate using check weights, using the scale often during a reloading session to verify charge weights, and looking into every case before you seat a bullet.
