Can a single cable type do the following
You don't want cable at all here, but individual wires instead

Pulling cable down a conduit is a waste of time/effort (as it's a pain in the rear to pull by all accounts I have heard) and fill space (as the cable's treated as round instead of oval/flat for conduit fill purposes).

Instead, what you want to be using are individual conductors -- the 200A-sized run can be made using 3 4/0 Al XHHW-2 wires for the phases and neutral -- this consumes much less fill than a 4/0-4/0-4/0-2/0 SER cable (529mm2 for the individual wires vs 1135mm2 for the cable) and is cheaper than the cable too, as you can use the EMT as an equipment grounding conductor here.  Given that you can remark wires 4AWG and larger freely to neutrals with a wrap of white electrical tape at the terminals as per NEC 200.6(B), a single 250' spool of 4/0 Al XHHW-2 will get the job done here.

As to that Al to Cu splice...

The Al to Cu splice, by the way, should be made up using 2-port, Al9Cu rated mechanical splice connectors ("Polaris", "Unitap", or equivalent).  These provide a reliable and rugged connection when torqued to specification with a torque wrench, which is a requirement in the NEC nowadays (as per 110.14(D)) in addition to being good installation practice anyway, and are simple to install (compared to split bolts).  You'll also want to use an inch-pound torque wrench on the breaker and panel lugs as well.