Pssh, yeah. That mnemonic is very helpful, but I had gotten the basic idea the first time. I just am stuck pulling myself in seven directions at once to work on all of the projects I've assigned myself to and my college work, so that's why I didn't get around to responding. This project isn't dead, though and I like that system of number notation because I think it's very clean and natural. As per the stroke to make the rune unalterable, I'm thinking just one vertical stroke down the center of the rune. It's very hard to mistake and it doesn't interfere with the current setup of the rune. (Though, admittedly I'm not sure how much it helps with the issue. ) As per approximates, I see no reason why there wouldn't just be an "unknown digit" rune. There is in the actual game mechanics: "?". Granted, it can and probably will be argued that that's just a translation convention.
As per the less accurate book keeping methods, methinks that this could boil down to number of significant digits according to the bookkeeper, e.g. 5-X if 5 is the five rune and X is a rune meaning "thousands place" with the hyphen being some kind of signifier of approximation. Basically "It rounds to 5000" or "About 5000" or "5000 and some." Which saves space and aids readability (slightly) from the bookkeeper's perspective. However, a bookkeeper could be ordered to treat all digits as significant: 5362 Barrels of Dwarven Rum is exactly 5362 and is written with a digit for each place value in stead of "5-X barrels of Dwarven Rum". ( The practicality of such simplifications is more obvious when you have hundreds of thousands. ) Though, I am still willing to posit that Dwarven bookkeepers use their own system of stenography for the purpose of rapidly taking notes and have a separate tally system that better facilitates addition rather than simple display of number value. ( In fact, bonus points if said tally system is impractical for displaying number value easily. There's a reason bookkeeping is a skill. Even real-life accountants have historically had to treat numbers differently and learn different maths than other professions. ) However, even if this is the case, it doesn't necessarily mean much linguistically as it does culturally/practically, as their records would probably still be translated into a Dwarven number system that all Dwarves can read instead of the specific bookkeeper/another bookkeeper. It's just how I visualize it and how I'd do it if I had to count everything in a fort.
Also, I'm looking at your runes and thinking to myself that they need to be simplified or at least given a cursive form. Sure they can all be written in 1-3 strokes, but those strokes look kind of awkward for a hand and don't inherently leave the hand in an optimal position to go to the next letter. ( Assuming dwarves write left-to-right, that is. ) It's not horrible, but a necromancer who was writing his fortieth biography definitely wouldn't use that, nor would any dwarf who had a lot to write, due to the extra movement increasing hand strain. In addition, the consonant runes wouldn't lend themselves very well to being engraved as of their most recent iteration. The worst offenders are the second and fourth rows, as well as special mention to the third character on the first row and the last two of the last row. ( The last of the last being more of a minor annoyance than a legitimate problem. )
Curiously, it seems like most of the number runes are actually suited to best being written by the hand that their spokes are mapped to. I'm not sure if this is relevant, but it suggests to me that a particularly skilled bookkeeper could write two at once, one quill in each hand, and potentially even take note of two numbers at once.