Well rather than leave this up in the air, it seems all the vehicles and equipment were abandoned on the island after the tests.
As to whether the two Constructors are still there, this is as far as I have been able to get -
Here is an extract from the log from a boat's voyage in 2000, describing the remains on the island -
Driving around this surprisingly large island, we noticed that the scenery changes slowly, the horizon consisting mainly of row after row of non-native coconut palms, splendid in their windblown greens and yellows. Our first stop was not what you would expect on a coral atoll. Christmas, unlike Tarawa the country's capitol, was never a battleground but was used as a base for the Allied Pacific Air Command in the Second World War. Remnants of the occupation are everywhere, great piles of abandoned equipment have been left to rust, permanently marring the landscape. This includes more than 1 million steel drums, along with tons of machinery scattered among the palm trees. Military facilities were extended when Christmas was chosen as a base for British and U.S. nuclear bomb tests, as were many desert atolls of the Pacific Ocean region, as they appeared to be vast empty spaces. We stopped at the detonation sites of the British tests viewing the hooks that anchored the bomb before the release of the balloon that carried it into the atmosphere, and the bunkers from which the explosions were viewed. Radiation tests have subsequently been carried out on the island, which apparently bares no ill effects. However we were told of the millions of birds that were killed and the island inhabitants taken aboard Allied ships and shown movies during the detonations and shortly returned to the island. Fortunately, the British Government has finally taken responsibility and are sending in a cleanup team in April 2001 to remove their equipment.
So it looks likely that the Constructors were removed (scrapped?) in 2001 as part of a cleanup operation. There was also a US operation to remove their kit sometime before 2000.
And from a different source - a picture of a row of Phoenix Model PA bitumen sprayers, used in the constructon of the test area, awaiting clearance as part of the cleanup operation (sorry, this is as close as I've been able to get!!).
Tar boilers - another 'first' on HMVF :-D