A P2X rating is specific to an aircraft and no you cant get a rating for a 340 and then use it to fly a 777.
If you get a P2X rating on a 747-400 you can fly the type you got the rating on but would then need to do a differences course for the freighter, the ERF, the converted pax to freighter aircraft and so on. Once you had completed the differences course and passed the test you can fly the other types of 747.
The only exception to this in CX is the Airbus. You do the P2X rating for the A340 and also used to do a differences course for the 340-600 (obviously not anymore). Once you meet the minimum experience required to do the CCQ course (200 hours in the 340 and a specified number or sectors) you go on an A330 course, do a sim and a line check. Differences courses do not require any simulator of line training/checks but the CCQ does. It takes a day as the aircraft are very similar for the ground school for the CCQ.
You can sometimes chose what you upgrade onto other than the 747-400 as they do not upgrade SOs on that fleet, think they have done in the past but only guys with extensive jet experience prior to CX. You can sometimes turn down a course saying you want to wait for the 777 for example but sometimes they say no you do this one. Currently I doubt anyone would turn down any course as progress has really slowed and who knows how many months would be the wait for a different type.
Yes lots of 777 on their way but this does not mean everyone will upgrade onto it. Lots of FO's want to move to the 777 from the airbus as the rosters are better so they may do that and then SOs upgrade onto the bus to take their places.