As with every time this question appears, ask yourself this:
Did the two manuals have the same gun for testing?
Did the two manuals have the same bullet for testing?
Did the two manuals have the same lot of powder for testing?
Did the two manuals use the same lot of primers and the same case head stamp/lot?
Did the two manuals use the same COL?
Unless every answer is YES, I guess there will be a difference.
Looking at my data compilation, start loads for 124-125gn lead bullets and 540/HS6 range from 5.0-5.9gn and MAX loads (all pressure tested per manuals) range from 5.5-6.6gn, so your load is 0.1gn under max pressure in one manual. So, one manuals found that 6.6gn was max, so they used a 10-11% drop from MAX for a 5.9gn start; however, other manuals reached max pressure before even that START load such that, if your mix is similar to those manuals, a 5.9gn start would already be over-MAX in your gun with your mix of components.
I always start with the lowest starting load I can find and work up in increments--usually 0.2-0.3gn steps. So, I would have worked up 5.0, 5.3, 5.6, and 5.9gn and only gone up from there if accuracy was improving and there were no pressure signs.
Starting loads: look at your manuals. Most starting loads are selected as follows:
1) A simple 10-12% reduction from the max load
2) manual starts at a velocity, so all start loads are the same velocity
3) manual starts at a pressure, so all start loads are the same pressure
Start loads are not minimums nor do they represent loads that will function your gun.