I am not an expert in this type of roofing, I do however have some questions and recommendations that may help you get the right answers.
First the questions. Is this roof drained with an internal system or scuppers along the edges? How large (square footage) is this roof? What part of the country are you in? Have you consulted an industrial/commercial roofing specialist?
Here in the north country, most flat roofs on larger buildings are treated in a bonded/welded rubber, neoprene membrane. All the edges, sidewalls, plumbing vents, chimneys etc must be properly flashed and sealed with bitchethane and bonded to the flat covering. It is also very important to know that a flat roof is actually not perfectly flat. They must have some designed pitch to a drain point/s. Any area that allows standing water is potential source for leaks. Proper drainage is essential and will prevent the majority of future leaks.
Since access to the roof seems to be an issue for you and the contractors you have consulted so far, consider the following:
Only deal with a contractor that owns or regularly uses a bucket truck or man-lift and is used to working on taller buildings, and has the proper safety equipment and trained personnel to safely handle the job and materials.
Look at options to install a dog house access on the roof. If there is no common area where one can be installed, explore the possibilities of an external attached caged ladder. Some method of easy access will allow safe, quick inspection of the roof.
Solving your problem should be fairly evident to a competent industrial/commercial roofing contractor. You may not like the answers you get, or the costs to fix the situation, but if you do it right this time, you will save money in the long run, minimize potential interior damage, and protect the value of your property. Good luck.
I mostly agree with Ed Beal. Small or hairline Cracks like C1 & C2 can be simply Caulked for a 10-plus year repair & yes you want to address all of those types of cracks whether they're on the wall or roof, so they don't become bigger cracks. You've got hundreds & ALL cracks are potential leaks.
Break-outs & fully open large splits & spalls like D1 & D3 need to be cleaned of all loose debris & forcibly filled with Hydraulic Cement, it slightly expands within & behind as it cures to make the best water-tightness & backing of the surrounding cement.
Areas like P1 that are in the field of the roof need to be leveled to each side of the low spot's high spots, pitched. Meaning, the P1 outside edge further from H1 will & must be slightly higher than P1's inner closer edge to H2. The entire roof should be shaped like 2 bath tub bottoms with H1 & H2 being the drains.
P2 is quite a bit different since it's blocked by a wall. P2 must be pitched into the roof field with the area at the back of the wall being significantly higher than the area at the front end of the wall. At the front end of the wall P2 then needs to be pitched inward or toward H2.
Your roof must tilt from the front to the back & must also be bellied down from the center & outside walls while always maintaining that front to back pitch in order for H1 & H2 to remove all water & have no puddling. Then, everything can be re-painted & the roof can be sealed.
Best Answer
2" deep puddles on a flat roof are a definite problem, and imply at least 16 feet of problem if the minimum 1/8" slope to drain is to be restored/preserved/maintained. And if that makes new puddles, even more area needs to be fixed.
I'm not clear on your (non-described) process, but this mess seems ripe for building up a proper surface with rigid foam and a new membrane, rather than jacking the roof boards from underneath, if that's what you have been doing.
Regardless of process, the entire roof surface needs to slope at least 1/8" per foot towards the drains. No part of the roof should actually be "flat".