Backup Lights and Wires (2013 Three)

So, I decided to replace the backup lights on my 2013 Prius Three, but two somewhat related issues came up that I’m hoping I can get some help with:

I ordered the lights attached.

They look cool and I was super excited to light up the heavens when I put it in reverse, but when I went to install them, I encountered a couple issues.

1) Is there any way to lengthen the wire? The wire going from the bulb into the depths of the car was long enough to fit the regular-sized bulb in and NO LONGER. Not a millimeter longer. Because of this, I did not have enough wire to put the much longer bulbs into the slot.

2) Because of this, I thought I’d be smart and try to put the bulb into the slot first before attaching the wire. This did not go well. The bulb slipped from my fingers and fell into the depths of the housing for the light. Any ideas on how to get it out that doesn’t involve removing the casing?