Type inference for object calculi S and S_\forall of "A Theory of Objects"

What is known / expected from the state-of-the-art on type inference for
implicitly typed (a la Curry) counterparts of the second-order object
calculi S and S_\forall (16.2 and 16.3 of the book "A Theory of
Objects") by Abadi and Cardelli?

The calculus in the paper "Type Inference with Simple Selftypes is
NP-complete" by Jens Palsberg seems close to a Curry counterpart of S
with neither variances nor self type parametric elder variable in
What essential differences / challenges are foreseen in tackling S or

The only other papers on type inference for Abadi and Cardelli's 
object calculi I know of are Palsberg's "Efficient Inference of 
Object Types" and Henglein's "Breaking the n^3 barrier". 
Any other references relevant for inferring types of Curry variants 
of S or S_\forall?

Luis Dominguez