You do not need genetically engineered humans, normal humans suffice.
Pressure is apart from the lungs not a problem for humans because our body is filled with fluids which are only very slightly compressible and pressure does not influence proper functions. Our bones are solid, but as the pressure comes from all sides, they also don't break or are impaired.
So fill the lungs with a breathable fluid and humans can withstand extreme pressures.
While the movie The Abyss portrayed the idea, many people think it is
science-fiction. It is not, breathable fluids like perfluorocarbon are existing and can be really used for this purpose.
So, what you need is an deep-diving apparatus.
The human sets up the gear. He breathes or gets an injection which
makes him unconscious (You could do this consciously, but it would be
torture). Then the gear fills slowly the lungs with a breathable fluid
and the gear inserts foldable tubes into the trachea/lungs.
Those tubes act as amplifier for breathing. The problem is that a human
cannot breathe deep enough to circulate the fluid, so the gear register
your breathing and the tubes amplify the breathing to mix the fluid
accordingly and replenish it with oxygen. Breathing is therefore only
limited by the amount of oxygen. With a nuclear battery and therefore
essential limitless energy, the necessary oxygen could be produced by
seawater and allows unlimited access.
After diving, the human gets unconscious again, he is laid with the head down on a stretcher to pump out the liquid, the gear pumps the fluid outside, collapses and retracts itself and can be taken out. Task finished.
Some remarks to the criticism by Arno Germond: All those points with the exception of High Pressure Nervous Syndrome (HPNS) has nothing to do with liquid breathing, only with the normal gaseous breathing and are therefore literally pointless. To allow breathing, the gases must have the same pressure as the outer water and because oxygen gets toxic with too much partial pressure, the only necessary component oxygen needs to be replaced with nitrogen, hydrogen or helium. This gases are dissolving in the bloodstream/body fluids and are causing unpleasant phenomena like decompression sickness when it bubbles out under lower pressure.
These phenoma do not appear in fluid breathing because there are no other gases than oxygen needed. HPNS is triggered by pressure, but can be counteracted with narcotic gases (you can either use hydrogen as second component or invent a new stabilizing substance which adapts the nerves to high pressure). If the diver emerges, there are no other toxic gases in the bloodstream and therefore no decompression effects.
Middle ear and other air containers (Paranasal sinuses) must be also filled with liquid via Eustachian Tube and sinus openings. Perfluorocarbon is non-toxic and the middle ear is able to remove liquids from the ear. In that case no problems with breaking eardrums are encountered.
I am not a doctor, but I am not aware of "accumulation of toxins" or "high pressure inhibits proper cell functioning". The cells are not shrinking (volume reduction is almost negligible for fluids and solids) and high pressure does not change the reaction rate for solids and liquids (!).
Granted, there will be likely unknown negative effects which will happen in depths of over 1 km in reality, but as long as they are unknown you can ignore them for the sake of the story you are writing.