I'd probably try a couple of methods which may or may not help. In welding, the welds are often alternated from one side to the other, as the cooling phase causes distortion. The alternating method minimizes distortion.
Another method that I'd consider, would be to raise some of the axial-lead components slightly above the board surface, where space permits. A shim of file folder material may be enough to leave a small gap, so the lead positions wouldn't be so rigid. (the shim removed after the solder cools).
Jumper wires (soldered with a shim underneath them, or a slight hump) placed laterally where they wouldn't interfere with other components or signals, may add some flexibility to the overall assembly.
-- Cheers, WB .............