It's not clear if you want your Day 1,2,3 to be stopovers (ie > 24 hours) or you just want day time fights. Most through flights are usually one day flight connecting to an overnight flight (which is not what you are seeking).
Using QF points will restrict your options - but perhaps you have sufficient to get to/from Asia - as mentioned above DPS is one of the 'cheaper' options.
As a fan of SQ - I like their day flight to SIN followed by an overnight layover (< 24 hours) then a day flight to FRA - you can then connect or catch a train to VIE). Unfortunately the day fight to FRA is > 12 hours so may not suit you - but there may be other options ex-SIN via the Middle East (but I find many flights ex-ME are at unsociable times and/or require very long daytime layovers).
