I agree with both the comments above. You won't NEED to fix the bulb inside the viv it will work fine how it is but as bluemoon has said you need to move your thermostat probe further from the heat source in order to increase the light output. It can be quite handy having the bulb external so you can make use of the full height without getting dangerously close to the bulb. You also obviously have a gaping big hole in the roof of your viv at the moment so I would try leaving it as it is for now and moving the probe.
On another note, I'm sure you've only created that tall basking structure to get close to the bulb but it looks far too dangerous to me, if one of those large rocks were to shift when your BD is climbing them it could easily result in a trapped and then broken leg or some other accident. I wouldn't stand that one rock so high and have it more parallel to the floor like the others so there is less chance of movement. Alternatively you could recreate fake rocks out of kingspan and grout. These will look brilliant and weigh in next to nothing.
Try moving the probe to the cooler end and report back.