If you leave Manchester early you could get to Munich by late evening.

Manchester - London by 1000/1100 (0600 - 0700 dep)

London to Brussels (Eurostar) by mid afternoon Target 1100 - 1200 train

German ICE from Brussels to Frankfurt arrive mid evening (Via Cologne) (Every 2 hours) 

Frankfurt to Munich (ICE) by late evening. (Many trains)

I would probably stop in Cologne for the night and head for Prague midday of day 2 - The Cologne cathedral is right by the station.

Hotels can be cheaper than sleepers, hostels are as cheap as couchettes.

Others can advise on sleepers but there are none in the UK from Manchester ) Only about 3 hrs to London.

OOI we go in a few weeks flying from Leeds to NIce, 2 nights Monaco, train to Venice for 2 nights, train to Vienna for 3 nights , 2 day trips, then Prague for 2 days and fly back. 5 pass travel days.

So your planned 9-11 days is easy to achieve. By the way Nuremberg is worth a full day.

Iam not sure but maybe next year finally the European Sleeper starts They plan to operate a Nighttrain from Brussels via Amsterdam Berlin to Prague (They planned to start Spring this year then Summer and currenty they have no new date given) Website of them 

Another option would be to catch a Eurostar to either Amsterdam (daily Nighttrain to Vienna), Brussels (certain days per week) or Paris (certain days per week) to  Regensburg (earlier connection to Prague), Linz (my choice if iam heading to Prague) or ofcourse to Vienna itself and start there.