My 2p worth...
I have an E91 (previous shape 3 series touring) which has decent boot space, but I wouldn't want to use it for moving house. While it's perfectly practical for getting large boxes and the like in, you'll struggle badly with any large'ish furniture.
It looks like you probably have the budget to get into an F11 (current shape 5 series touring) and this is where I'd put my money, especially for your particular requirements. They are very large (substantially bigger than 3 series and C class size), very well made, and very comfortable.
If you want performance then the 530d is the right choice. If you're not too fussed about performance then I'd opt for the 520d. It offers much better fuel economy and you'll likely have a greater choice of cars to pick from.
The 520d is no slouch and the 530d really is very brisk, but neither engine will offer you performance comparable to your Z4.
Also, the 525d is now a 2 litre 4-pot diesel, but I'm not sure when that happened...it may be that in earlier F10/F11 the 525d was still the 3 litre 6-pot.
/edit: Seems that the F10/F11 525d was 6-pot in 2010/2011 and changed over to the 4-pot in 2011. Therefore, models in your budget will have the 6-pot engine.