Guys/gals, don't waste your time with random search, random mode etc, there is no such a thing as "random" all events follow a pattern, we as humans have to interfere and change these patterns, by following logic and the power of our minds.
Instead of "hoping" for a "lucky" hit in a random search, start working on ways to find a stride for public key brute force.
Example:
Target = 127654 (unknown) we only know it's between 100,000 and 200,000.
So we subtract it from 200,000 - 127654 = 72,346. Now we are certain our result is 100% smaller than 100,000 (start range), but since we don't know how much smaller, we'd just subtract it from half of start range, 50,000 - 72,346 = 22,346. And now we are 100% certain the result is smaller than 50,000 but we don't know how much, again we subtract it from 1/4 of start range 25,000 - 22,346 = 2,654.
Now tell me what do you see?
127654
2654
127654 - 2654 = 125000
What you need to work on is figuring out a stride to add to 125,000 till we reach our target, whether we add 13 at each step, 14 or 15, what happens when we reach 127698? Can we save the keys between 127654 and 127700 so when we are adding stride and land on one of the saved keys, we know right away and easily solve the key or not?
These things should be your priority, enough of running this tool/script and that tool/script, come up with an algorithm which doesn't require "random" and "luck" but requires math equations and numbers.
Sorry man, this either will not work because you went around the curve, or you will have trillions^trillions of strides to go through/take.
Your example:
Target = 127654
range = 100,000 - 200,000
Like you said, we do not know the target, only the range.
So let's say the target's key is 199,999
Watch the math:
200,000 - 199,999 = 1
1 - 50,000 = -49,999
-49,999 - 25,000 = -74,999
You have now went backwards around the curve. So now, you can't even start your program to start striding from 0 or 1.
But let's deal with your math above and talk about the strides.
It's ok when a range is only 200,000 but now imagine a much larger range, say 2^130. If you have a stride of 13, 14, 15, etc., it will take you more than a lifetime to still get through that range.