I don't know anything about Diff speakers but...
The impedance of a speaker tells you nothing about its "quality". There are fantastic 4ohm speakers and lousy ones; same for 8ohm speakers. The only issue is that 40hm speakers are MUCH harder to drive than 8ohm speakers. Most decent receivers will drive 4ohm speakers but when pushed real hard, the amp will heat up considerably or even shutdown. The Yamaha will probably drive them but be careful with the volume control. If you can't obtain the volume you desire or the amp gets insanely hot or shuts down, you will need to get a receiver that is rated for 4ohm speakers or move to a separate amp.
The fact that your friend's Yamaha can drive similar speakers to louder levels likely has nothing to do with the receiver - there are so many other factors. Maybe his room is much smaller, he calibrated the levels properly, or his Diff speakers are actually a lighter load than yours.
If you like your Diff speakers and want to keep them I would look at a receiver rated for 4ohms. The Yamaha doesnt have a 4ohm switch because they dont want you to drive 4ohm speakers. Even if it did have one, you don't want to use it as it limits the current - just be mindful of the volume control as said above.
I don't know the conversion rate from AUSD to USD but $2kAus still sounds like alot of cash and I wouldn't want to just trash it and buy another one. Buy one that is suitable for your needs or trade those speakers in for 8ohm speakers.