Interesting take on the situation.
Generally though it is thought that gravity will and should have merged our local group by then.
Maybe, I have not cared. The question would be why should it merge them at all? The Solar system is quite stable over a long time. So, gravitational configurations stable over long times are obviously possible.
Or are you promoting a "Big Rip" scenario some trillions and trillions and trillions of years into the future, where [if I'm reading you correctly] the acceleration in the expansion rate will continue unhindered, and even local groups will be ripped apart, solar systems ripped apart, so overcoming gravity, and even the strong nuclear, weak and EMF's eventually overcome by the acceleration in the expansion rate and we would all be ripped apart.
If there is really an acceleration which is visible now, and if it is described by Einstein's cosmological constant, then this would be unavoidable. No reason to promote it, and I don't. But this would be the mainstream prediction. And if I don't mention the theory which I use, I mean the mainstream theory.
Not sure if this are "trillions and trillions" of years (again, not cared). The expansion would be exponential. And that means that one needs more time for this than the universe exists, but not that much more. But, ok, a factor 100 is not unreasonable, and this would be already trillions.
The Wiki is correct about a rather old state of the mainstream opinion, before acceleration was accepted mainstream. For $\Lambda>0$, which is actually the mainstream opinion, everything else like the curvature becomes irrelevant.
What I would promote is an alternative, (but don't worry, a published one) proposed by Wiltshire, the timescape scenario. In this approach, the accelerated expansion is simply an error of the homogeneous FLRW approach. One has to take into account that there are now big voids, that light is differently redshifted inside the voids, and that we are not in a void. Essentially, the inner parts of the voids expand in a faster way, but if we ignore this, and use a homogeneous model, these differences will be misinterpreted as an accelerated expansion. If we would sit in the center of a void, and evaluate it similarly homogeneously, it would look decelerating.
The funny thing is that there are now published papers which compare above scenarios. They are not decisive. But nobody questions the computations themselves. This is very strange. Given that taking into account inhomogeneity would lead to a fake acceleration, it should be already clear after this that pure FLRW is inappropriate to evaluate the question if the expansion is accelerating. What one would have to do to evaluate $\Lambda$ would be to consider a $\Lambda$CDM inhomogeneously to identify its size and the error bars. To continue to consider $\Lambda$CDM in the homogeneous FLRW ansatz is, once it has been found out by computations that inhomogeneity has some effects, already bad science.