Reducing to "physical properties" is not necessarily the same as to "the physical properties of the ingredients".

Well, no, but reducing to the properties of (and some suitable well behaved set of relations between) the smallest ingredients is what reductionists mean by reductionism.

I would have thought physicalists think mental properties can be reduced to physical properties, but reductionists identify these with the physical properties of the ingredients

I would have thought reductionists think they can be reduced and identity theorists think they are already identical.

I suppose one way of looking at it is that when you say "in principle" the principles you refer to are physical principles, whereas when emergentists see obstacles as present "in principle" when certain kinds of complexity are present they are more properly described as mathematical principles.

"in principle" means in the absence of de-facto limits in cognitive and/or computational power.

Mental events can certainly be reduced to physical events, but I would take mental properties to be the properties of the set of all possible such events, and the possibility of connecting these to the properties of the brain's ingredients even in principle is certainly not self-evident.

Errrr...you believe in Token Identity but not Type Identity???