Practical Data-oblivious Compaction?

Compaction is a particularly weak form of sorting. The problem can be phrased as follows:

Given an array $A$ of $N$ cells, with at most $R$ of the cells distinguished (say by a bit), produce an array $D$ of at most size $O(R)$ containing all of the marked cells

Compaction is said to be:

• Tight: If the output array $D$ is of size exactly $R$
• Order-preserving: If the relative ordering of marked elements of $A$ is the same as the relative ordering of elements of $D$ (i.e. if the compaction is "stable" in the sense of sorting)
• Data-oblivious: If the algorithm which computes the compaction has access patterns independent of the data

One can construct tight, order-preserving, data-oblivious compaction from a sorting network. You have to use non-standard comparison function which:

• Sets all marked elements as greater than unmarked elements
• Within comparisons between marked elements (resp. unmarked elements), breaks ties by the element’s initial ordering in the array.

But such a function is easy to specify, and can be computed in $O(log N)$ time.
This means that one can construct tight, order-preserving, data-oblivious compaction from the AKS sorting network (giving an $O(N(log N)^2)$ algorithm) or from a more practical sorting network like Batcher Odd-Even Mergesort (giving an $O(N(log N)^3)$ algorithm).

Anyone who has worked for sorting networks before has heard that there are the asymptotically optimal algorithms (namely the AKS sorting network and ZigZag Sort, both using $O(Nlog N)$ comparisons), and the practically efficient algorithms (Batcher’s mentioned above is one example, but there are many which are $O(N(log N)^2)$ comparisons).

I’m essentially curious if there is something similar for compaction — I have seen papers such as this which give oblivious tight compaction in $O(N)$ time <1>.
This paper’s improvement is lowering the implied constant from $2^{228}$ to ~$9000$. I imagine that for al "reasonably-sized arrays" it is still more efficient to pair Batcher’s sorting network with the aforementioned non-standard comparison function.

So has been research done into practically-efficient compaction algorithms? While I eventually want something which is tight, order-preserving, and data-oblivious, the most important keyword by far is "data-oblivious". I’m willing to tolerate a negligible (meaning $N^{-omega(1)}$) probability of failure, as long as it has "good constants".
Moreover the data to be compacted is "random" in a strong sense. In particular, each element of the array is marked/not marked according to the result of an i.i.d. $mathsf{Bern}(1/2)$.

<1> The linked algorithm has a negligible probability of failure, which is fine for my purposes.