Have a look at the table on the lower right side of the first page in the link in post #9. Any manufacturer I have ever spoken to specifies trigger pull as: Total Trigger Pull = 1st. Stage Pull + 2nd. Stage Pull
The reason is because on a proper 2 stage trigger, adjusting one stage will not affect the other stage (which means they are additive mechanically as well). Adjusting the 1 stage will not affect the delta between where the second stage wall is encountered and where the trigger breaks, and vice-versa. If you put 5 oz. on both stages, you will have a 10 oz. total trigger pull. If you increase the 1st. stage to 10 oz., the total trigger pull will be 15 oz. (still a 5 oz. difference on the 2nd stage). If you increase the 1 stage trigger pull to 15 oz., the total trigger pull will be 20 oz. (still a 5 oz. difference on the 2nd stage). So, it kind of makes sense to specify the weights that way.
I'm guessing that you're shooting F-Class or something that doesn't require you to pick up 1 or 2 kg trigger weights since you're talking about a total trigger pull of 8 oz. The trigger in question can't go below 1.5 lbs. total pull weight, so it's probably not well suited to your application to begin with.
As for pulling through the second stage; on a good trigger, increasing the weight does not change the smoothness of the pull. Pulling through may be an issue when your dealing with triggers in low ounce total pull weights, but it's a common practice in disciplines where we have to have a trigger set to a total pull weight that is reasonable for field use for the first stage to account for bulk of the total pull weight. You adjust the 2nd. stage to where you don't fire unintentionally, then increase the 1st. stage till you can pick up the trigger weight with some margin. So in your terminology, my trigger has a 29 oz. 1 stage and a 40 oz. second stage for a total pull weight of 40 oz. I have never had an issue unintentionally pulling through the 2nd. stage with those settings shooting the rifle offhand, off of various barricades or from prone. I would suggest that someone who would lacks trigger control, and needs to do a bit more dry fire practice to hone their fundamentals.
The reason it's set that way is because it allows me to pick up the specified trigger weight, but doesn't feel like I'm pulling the total weight. It only feels Like I'm pulling the difference between the 1st. stage and total trigger weight (the 2nd. stage pull weight - also why the trigger weights are specified like that). If I set my 2 stage CG Xtreme to 29 oz. 1st. stage / 40 oz. total, after I take up the 29 oz., it feels like an 11 oz. trigger when I break the shot. If I compare it next to a Jewel set to 40 oz., the Jewel feels like a 40 oz. trigger when I break the shot. Both require 40 oz. total to break the shot, but the feel is completely different and it shows on the target (especially when shooting offhand or from an unstable position).