How do you encode Lamping's abstract algorithm using interaction combinators?
I am not aware of any implementation of Lamping's algorithm directly in the interaction combinators.  I do know that the presence of integer labels is a necessary feature of Lamping's algorithm, even for EAL-typable terms, because the labels reflect the nesting of so-called exponential boxes in proof nets, and Lamping's algorithm is essentially the execution of proof nets using the geometry of interaction, as first observed by Gonthier, Abadi and Lévy.  So the question of implementing the algorithm in the interaction combinators boils down to representing exponential boxes in proof nets using the combinators. This is essentially what Mackie and Pinto did in their paper.

Of course, Mackie and Pinto's encoding adresses all $\lambda$-terms, which use full linear logic boxes, whereas EAL-typable terms use elementary linear logic boxes, which are simpler (they are so-called functorial boxes).  However, I do not believe that this simplification would have a notable impact on interaction combinator implementations.  This is because boxes are a global feature (they identify arbitrarily big subnets to be duplicated/erased), whereas the interaction combinators (as any interaction net system) are completely local (reduction only modifies bounded subnets), so the challenge is to represent such global features locally.  Now, global duplication/erasing in EAL is identical as in full linear logic, that is why I do not expect that an interaction combinator implementation of EAL would radically differ from the one proposed by Mackie and Pinto.