I dug around and did a little more research. I reviewed the FAA Inspector's Handbook to see if there was any guidance. I couldn't find any (which doesn't mean there isn't). Because a large portion of part 61.55 is new this year I suspect the question hasn't been asked formally yet of the FAA and an interpretation given.

That said, after reviewing the two regulations again and various definitions, I'm reversing myself.

Part 61.51(e) Logging pilot-in-command flight time. (1) A sport, recreational, private, or commercial pilot may log pilot-in-command time only for that flight time during which that person --
(i) is the sole manipulator of the controls of an aircraft for which the pilot is rated or has privileges;...

In the past "rated" had be defined by the FAA to mean "type rating" as defined in part 61.31 and in part 61.1 definitions. This has ment a "PIC type rating" as that was the only type available. With the advent of the expanded rule for second-in-command type ratings in part 61.55, I wonder if, with respect to 61.51(e), if that definition would change to "any type rating".

In 61.55(d) and (e) the regulation refers to "SIC Privileges only" pilot type rating. Both those words, rated and privileges, are used in 61.51(e). And 61.51(e) allows you to log PIC time for the purposes of a certificate or privilege (that's 61.51(c)) as sole manipulator, as long as you don't have an ATP.

So I think you can log PIC time with an SIC Privileges Only Type Rating when you are sole manipulator of the controls. However, if you are relying on that time to meet the minimums for an ATP certificate, I would get an interpertation from your training department or an FAA Inspector.