Testing for differential ranking between lists relative to a reference list I am interested in comparing ranked lists in order to find elements that are differently ranked. Suppose we have 10 lists, each ranked (and for simplicity assuming the elements overlap and only the ranking was different). What method could I apply to find elements with high ranks in list1 that consistently have low(er) ranks in all the other lists?
The background here is that each of these lists represent outputs from differential testings from experiments that cannot be directly compared to each other as confounders exist between them that are nested with the effect we want to compare. Hence, I would like to at least prioritize elements that in the given reference list ranked highly (and therefore were very significant or "important" in experiment1), but have low(er) ranks in all other experiments, suggesting that this element was "unique" to experiment 1, meriting downstream experiments with these elements.
For elements consistently ranked highly I would use RobustRankAggregation or the Rank Product calculation, but what about actually finding differences in ranked lists? Obviously one could simply take the topX elements from list 1 and calculate something like the variance for their ranks across the other lists, but I am hoping for a method that is more sophisticated. If possible links to respective implementations/packages in R would be appreciated.

One possible way to approach your problem is as follows: For each element, collect all the ranks that it has in all your lists, i.e., if you have $n$ lists, $m$ elements, and the rank of an element $e_i$ in list $l_k$ is $r_k(e_i)$, then the rank collection $c_i$ of an element $e_i$ is:
$$
c_i := (r_1(e_i), r_2(e_i), \ldots, r_n(e_i)), \quad i=1,\ldots, m.
$$
Now you are trying to find the elements $e_i$ for which there is a list $l_k$ such that $r_k(e_i)$ is consistently different from the ranks $r_s(e_i)$ of $e_i$ in the other lists $l_k, s\ne k$. This can be understood as finding an outlier in the collection $c_i$.
In general, there are many methods for finding outliers $x$ in a set $X$ and most of them assign an outlier score $os(x)$ to each $x\in X$ which is supposed to describe the amount of "outlier-ness". And the most outlying $x\in X$ is then the $x$ with the maximum outlier score. So you could assign to each element $e_i$ the maximum outlier score $mos(e_i)$ of all the ranks in $c_i$:
$$
mos(e_i) := max_k\{os(r_k(e_i))\}.
$$
Then, all that is left to do is to find the elements $e_i$ with the largest value of $mos(e_i)$.
You mentioned that you want to find the elements $e_i$ which are not only differently ranked in one list compared to the other lists, but also that this outlying rank is higher than that in the other lists. If this is the case, you could simply append a filter to the outlier detection which would make sure that this is indeed the case.
Back to the outlier detection and available algorithms: Many methods are possible. E.g. you could take as outlier score the z-score, the distance of a rank $r_k(e_i)$ to the mean $\mu_i := mean(c_i)$ divided by the standard deviation $\sigma_i := sd(c_i)$:
$$
os_z(r_k(e_i)) := \frac{|r_k(e_i) - \mu_i|}{\sigma_i}.
$$
Other outlier detection methods with implementations in R are e.g. kNN or isolation forest. Of course, if you are willing to consider python libraries, too, there is a whole collection here. Most of those are, however, overkill, given that you have only about ten lists.
