So for a 6838 Ω resistor you are planning to use 6980 Ω, 634.o kΩ, and 715 kΩ all in parallel. I agree that this will give you nominally 6837.96 Ω. But the question is whether there is any point. I think you said you were going to use 0.1% resistors. That means that the tolerance on the 6838 Ω resistor is 6.8 Ω all by itself (which is going to dominate the tolerance range). If all of the resistors are at the lower end of their limits then the resistance could be as low as 6831 Ω while if they are all at the upper end of their limits, then the resistance could be as high as 6844 Ω, giving a tolerance of right at 6.5 Ω or just under 0.1% (not too surprising).
What if you just put three 20.5 kΩ resistors in parallel? That would give you a nominal resistance of 6833 Ω with a tolerance of that same 6.5 Ω and at least you could buy all the same values. The value you want is within the tolerance range of this combination, so is there any real benefit to trying to get the ideal value any closer?
I would say the tolerance is secondary to the stability. I would buy 10-20 of ea value and they can be sorted to get closer match, and if they are stable used in an air conditioned setting they should exceed other variables of the meter without requiring rescaling. I saw that Vishay makes an ultraprecision bulk metal trimpot also but at $66ea I'm not planning on that soon.