The construction industry (like any other) is full of people who find a single way to do things and will not listen to any alternatives. I do a lot of out-of-the-box stuff and have found more than a few contractors who refused to do things my way. A good example is hydrovac. The first time I needed to trench across a highly congested part of a compressor station, everyone I talked to said my only option was to shut down the station and relocate equipment. I searched around and found a company in another region that was doing hydrovac and they said that they could trench under the equipment in place and in service. Two local contractors refused to do the pipe part of the job (and I've never used them since), the third was uneasy but willing. The job went perfecty and now just about every job in this area has a hydrovac truck included somewhere. People's arguments agianst the process read just like the posts in this thread and they all boil down to "that's not the way we do it".
If I had to move a tank "a few inches", I'd certainly look at doing it with air bags. Cranes do an amazingly lousy job of moving a heavy load a short distance. With the air bags you never have the load suspended in air and subject to wind currents. Write a heavy-lift procedure with enough safety factor to account for the issues above (e.g., maybe use 50% more bags than necessary, manifold the air supply so all get air at the same time, specify a slow rate of pressurization, etc).
David