How long are the wire leads coming out of each LED to where you want the ends mounted?
If you can run the leads from each LED to some type of PC board so that they are all together, then you could easily solder them to the board. Doing it this way would allow you replace any burned out LED's by simply de-soldering the bad one and soldering in a new one.
You can buy the small PC boards from electric places like Digikey online. They come in a bunch of different shapes so that you can cut them down to exactly the size you need.
They also sell small enclosures that you can put them into, which would make it easier to mount behind the grill.
Here is an example of a simple PC board from Digikey. You can see that you can solder a bunch of wires or components into the copper busbar areas and have them all connected. Plus you can cut the board down to whatever size you need. This small board is about $6.00.
Jim