I've got the PoD in 1769. I want secession in the 1840s over an issue other than slavery.
How would you go about accomplishing this? Or would you say that it's impossible with a PoD in 1769, that is prior to the Constitution having been drawn up, prior to the Articles of Confederation having been drawn up, prior to the Revolutionary War having even started, to bring about secession over an issue other than slavery?
With a 1769 PoD, the short answer is "however you want". That's time enough for the *USA to change in so many ways that a secession could be over any number of factors.
The challenge, though, is creating something close enough to the OTL USA for the comparison to become meaningful. What you need is some kind of different federal structure so that secession over "state's rights" becomes a matter of tariffs/ economic policy/ settlement of western territories / pretty much any other combination of triggers, rather than slavery.
With that sort of PoD, you could even have a case of slavery remaining in place in some northern states, so any secession wouldn't be over slavery per se. There's so many options, it's more a case of seeing what general kind of goal you want to accomplish, then working out how best to change things to achieve that.