The piers that the first contractor suggested...are they a Helical pier sytem? If they are, they are usually installed by licensed renovation contractors and they normally provide all the engineering and installation. In other words they are the only ones that you will ever talk to and they may just be trying to sell you a pretty expensive system that you may not need because they could offer no other solution and of course it makes them the most money.
Once the helical piers are installed do they intend to lift the house to "repair" the cracks? Also what is the reasoning that they gave you for the piers? How deep is the bedrock in your area?
Secondly the soils engineer that you had come out did they hand auger or machine remove the sample from the same depth as the footing supporting your building? The contracting issue that the soil engineer is speaking of is dessication or drying of the clay. A one year drought is typically not sufficient time to remove enough moisture from the clay to make a large difference altjough small movements are sometimes evidenced. I hope that you engineer is testing for moisture content along with composition. Post the results when they arrive.
Again....Pictures of the situation would help greatly and would allow me to give you a reasonable idea of the problem.
Regardless of what the problem is the best thing to do is to get the area looked at by a mason so that you can get an idea of the cost for repointing the area. The mason may be able to give you some insight into the condition of your mortar and the general condition of your wall and you may suprised to find out that the mortar just needs to be repaired.
IMHO the use of remedial piers in a residential situation is kept for the really bad cases, due to cost. I am not saying that they are not a great way to repair a house but they should be used when necessary and it sounds like maybe what you have is some settlement that has gotten worse and could most likely be cured by repointing and maybe resetting some brick depending upon how bad it is. I am not trying to talk you out of the piers, especially if they are necessary, but just hoping to allow options that you can explore if you want.