Of course all of this is theoretical, but I would say no, because Karl Fritz made the pack with his Titan, so it's not just what the First King wants that is the problem. It's that the Titan itself is enforcing the will of Karl Fritz.

I think an Ackerman/Reiss child could ignore the Founding Titan and go ahead spilling all the secrets they wanted, because that does not involve the use of the Titan itself. But asking the Founding Titan to use its powers in a way that would not align with the First King's wishes would not be possible.

Youŕe actually making my argument for me. Suppose youŕe theory is correct and the First Titan is imposing the Kingś ¨pact¨ on the inheritor. This implies that the Coordinate´s power is the thing that suppresses the will to act, not the ideology itself. By that logic, anyone immune to the Founding TItanś machinations would, therefore, be free to act of their own volition, disregarding that of the Progenitor and the King. I´ve also read that any Coordinate inheritor is free to disseminate information at their discretion, but many (if not all) choose not to do so for their own personal reasons; their reluctance to share whatever secrets they´ve inherited along with the Titan has nothing to do with the Kingś Will or the Founding Titanś power.

Personally, i think the biggest hole in my theory has more to do with the inherited memory of the previous Titan incarnates. As far as we know, a personś personality and ideology is derived almost exclusively from the sum of their experiences. By inheriting the memories of others, oneś entire identity would change to some degree, radically or at least marginally. A perfect example of this is Frieda Reissś transformation from a loving, caring young woman, into a dogmatic, paranoid and volitile figure. It may be the case that any royal inheriting the Founding Titan and the memories of Karl Fritz could therefore be considered, at least to some degree, Karl Fritz reincarnate; his memories wouldn´t just include his experiences and ideology, but all the rationale behind it. Of course, this somewhat contradicts the fact that only royals are affected by the Kingś WIll and not anyone inheriting the Progenitor. Maybe it has something to do with ancestoral cellular memory, like in the Dune series.

We don't even know if Ackermans can become titans. Kenny's grandfather said they were a completely separate bloodline to the subjects of Ymir.

You would imagine most Ackermans alive in the present story must have subjects of Ymir in their family tree. It would be very hard for the Ackermans to only have children with other Ackermans given their rarity and how the modern Ackermans are mostly unaware of their own history.

Yes, this is true. However, the statements made above are entirely conjecture; theory based on the supposition that the Ackerman peoples ARE (at least, to some degree) Subjects of Ymir, and that they have the potential to inherit Titan Powers. It would probably be prudent to, in the future, avoid pointing out the inherently (and obviously) dubious nature of arguments on the ¨theories¨ board. All threads on this board make certain presumptions to allow for the various theories presented. Iḿ sure everyone involved in this board is aware that, considering that the base material has not yet confirmed these presumptions, they may not be true. That being said, however, the nature of theory is to use the information you DO have to present a thesis or hypothesis that is potentially viable within the boundries/parameters established by said information. As new information becomes avaiable, it is introduced into the argument and the hypothesis is tested; thus, it either remains viable or is disproven. Even though your argument is valid, pointing out that the initial presumptions of the central thesis are unvarified or potentially erroneous is counter-productive (and actually a little insulting). 

I also don't follow this idea of making the pact with the founding titan, as if it's a conscious being monitoring what its holders are doing and stepping in when they cross a line.

I viewed the vow more as a concentrated use of the titan's brainwashing powers that would preemptively apply to all future royal holders of the titan. It seemed pretty obvious that this was the case, due to the total change in personality experienced by the holders as soon as they received it. But maybe you know something I don't.

No, no! You've got it. That's pretty much the core of my theory. When someone inherits a Titan, it's not sentient or self-aware. The Titan and its host don't communicate; they're essentially the same being. This means that once someone inherits a Titan, their will is its will. However, here-in lies the problem. The new host will inherit not only the Titan's power, but all the memories of the previous hosts as well. It's my understanding, that Karl Fritz's "pact" was really his own ideology being imposed on not just the inheritors but the general populace (at least those not immune to the Founding Titan's manipulations). The idea behind "the King's Will" is that Karl Fritz's was so dogmatic in his ideology, that those who inherited his memories also inherited his convictions and all the rationale that goes with it. I suppose the reason that it only affects those of royal lineage is due to the fact that only royals can fully utilize the Progenitor's abilities; and as a result, they not only whole-heartedly believe in Karl Fritz's creed, but also (as a contingency) fall victim to the Founding Titan's ability themselves, as Karl Fritz, in effect, used it on himself to ensure his decendents didn't subvert or sabatage the punishment he established for the Subjects of Ymir. That's why i'm supposing that if a Royal / Ackerman coupling produced a child, and that child were to inherit the Coordinate, (considering people of Ackerman blood are immune to the Titan's mind control) they may be able to fully use the Titan's power while disregarding (or even overriding) the First King's Will.

Well it seems that blood ties have a significant effect on passing down th memory of the nine titans (cf chapter 95)
Gabi also add : "So... If I inherit the armored titan, I'm sure you will continue to live inside of me" (to Reiner)
So I think that the "King's curse" is based on this phenomenom.
And I would not understand why a Ackrman/Reiss guy would be exempted. (Assuming that Ackermans can actually turn into Titan)