How to keep an SSD in shape on Yosemite?
EDIT 3:

Yes! Since the release of 10.10.4, Apple now provides a new tool called trimforce, allowing users to activate TRIM also on unsupported disks. So now the ultimate and final answer is: 

sudo trimforce enable


/EDIT 3

EDIT 1: 

Finally I found a way! Apparently there is a neat trick hidden in the fsck tool as this answer says.

So in the future I will boot into Single User Mode (press ⌘+S at boot screen) from time to time and issue the command fsck -fy. It will check the disk and finish with the message Trimming unused blocks.

/EDIT 1

EDIT 2:

So there is a new tool called Disk Sensei that specializes on exactly that problem. It has a manual TRIM command and helps you turning Yosemite's kext signing on and off.

/EDIT 2:

Furthermore, I read about DiskFresh which would somewhat accomplish what I was originally asking for. This Windows (Bootcamp partition required) tool will rewrite all data of partitions or an entire disk. This approach seems a little less painful than wiping my SSD and restoring it from a backup. However, it also comes with the downside of doing an additional write cycle.