Let's take this by parts. When you state
There are no experiments with revised limits of the standard UP.
apart from being gratuitously inflammatory, when you actually look at that statement it means really very little.
The standard UP says that position and momentum can't be measured simultaneously.
That's not correct - it is a suitable summary of the principle but it's too rough for actual use. The uncertainty principle states that the product of the uncertainties in position and momentum, $\Delta x$ and $\Delta p$, on any state of the system, is bounded from below, i.e. that $\Delta x\,\Delta p \gtrsim \hbar/2$.
On a more abstract setting, given any two physical quantities $A$ and $B$, the product of their uncertainties is also bounded from below, but in the most general case the bound reads
\Delta A \, \Delta B \geq \frac12 \left|\left<[\hat A,\hat B]\right>\right|
and it is in terms of the expectation value of the commutator of the operators that correspond to those observables. This is standard fare in any introductory course in quantum mechanics, and it is the standard way to generalize the Heisenberg uncertainty principle to arbitrary observables; its technical name is the Robertson-Schrödinger uncertainty relation. As such, there's plenty of examples around - it's present pretty much any time you're doing quantum mechanics.
In the specific case of the Colangelo et al. paper, these uncertainty relations take the form
\Delta S_i \, \Delta S_j \geq \frac12 \left|⟨S_k⟩\right|,
where $S_i$, $S_j$, $S_k$ are any permutation of the three components of spin; the relation says that you can measure two components simultaneously so long as the third component averages out to zero. This relation is (a trivial consequence of) the cornerstone of the angular momentum algebra in quantum mechanics, and it is taught during any introductory QM course.
This is all to say: the "non-Heisenberg-ness" of the uncertainty relation at play in that paper is nothing new, and nothing much to gawk at. The paper represents important technical and technological achievements, but it does not break any previous conceptual paradigms.