You are nonplussed. You have encountered many and have collected many of those narrow type heatsinks on the right. But, all you want to do is cool down your hot house flower LEDs. It's time to FAB just the right heatsink flavour for the job. That flavour is the heatsink on the left.
Step 1: CUT AND STITCH METHOD
Your new fancy pants LEDs will enjoy the smooth flat surface of the heatsink on the left. Whoa.
Step 2: SAVE THE HARDWARE FOR LATER
This box of hardware came from no other source than taking-things-apart. This handful of machine screws was holding down the transistors on the original heatsink.
Step 3: MEASURE AND CUT
I'm lucky to have a good saw. Use a blade with carbide teeth and you will be able to cut through the soft aluminum heatsink material easily. Wear eye protection, and, YIKES, sometimes those aluminum chips are hot (wear long sleeves).
Step 4: JOIN TWO HALVES
In this case, I've taken advantage of the slots in the heatsink prepared to receive self-tapping screws. I'm inserting a screw into one of these channels.
Step 5: TWIST HALVES TOGETHER
We don't need the head of the screw, so off it comes. The two halves are rotated together to form a block, but we can't use this method on the other side, so we'll insert a pin.
Step 6: INSERT PIN
Before the pin is inserted, I'm filling the channel with a small amount of that 680 sticky stuff (made to hold nuts, etc., in place). I had some welding rod that was just the right size to snugly fit in the channel, and cut a piece just shorter than the full length of the heatsink.
Step 7: EXAMINE BLOCK
Here I have two heatsink blocks each made using this method. To increase thermal flow through the heatsink, you could additionally add some (typically white silicone-based) heatsink compound between the blocks. Now to see if our fancy pants (hot-house-flower) LEDs will be happy...