LUKS + LVM at Install Time

Question

I am trying to use the Ubuntu 14.04.3 LTS installer to create a disk layout that logically looks like this during installation:

/dev/sad
   |
   +-- /dev/sda1 (/boot)
   |
   +-- /dev/sda2 (LUKS)
   |     |
   |     +- SWAP
   |     |
   |     +- / (root)
   |
   |-- [ 60GB free space for SSD over-provisioning ]

I chose "Something else" when asked about disk partitioning and I think to achieve this that I have to use LVM, like this:

/dev/sda
   |
   +-- /dev/sda1 (/boot)
   |
   +-- /dev/sda2 (LUKS)
   |     | 
   |     +-- LVM
   |          |
   |          +- SWAP (logical volume for swap)
   |          |
   |          +- / (logical volume for root)
   |
   |-- [ 60GB free space for SSD over-provisioning ]

Basically, I want a single LUKS container that contains both SWAP and / (root) partitions so SWAP and root are both encrypted together.

I cannot find any way to set this up in the Ubuntu 14.04.3 installer. I can create the LUKS container, but it always contains a single partition under it and I can find no way to setup LVM within it.

I tried to setup LUKS and then quit the installer, use the LVM command-line and then go back in and install on the logical volumes, but I got a system that would not boot.

If there is a way to do this with LVM or even without LVM (maybe with btrfs for /boot and /, but not for SWAP since copy-on-write would suck for SWAP), please help.