d5 activates use of spherical basis set, which reduces the number of d functions from 6 to 5 per atom. This option will help you overcome (at least, partially) linear dependence problem.

Nonzero NZVAR activates optimization in DLC rather than cartesian coordinates. Erratic optimization in your first example was probably due to the use of cartesians.

As for your examples, I saw 6-31+G* basis on carbons and 6-31G basis on hydrogens, while your systems require 6-31G* on carbons (they all may be regarded as inner atoms) and 6-31+G* on hydrogens, because all of them are peripheral:

CARBON
S   6
 1   3047.5249000              0.0018347        
 2    457.3695100              0.0140373        
 3    103.9486900              0.0688426        
 4     29.2101550              0.2321844        
 5      9.2866630              0.4679413        
 6      3.1639270              0.3623120        
L   3
 1      7.8682724             -0.1193324              0.0689991        
 2      1.8812885             -0.1608542              0.3164240        
 3      0.5442493              1.1434564              0.7443083        
L   1
 1      0.1687144              1.0000000              1.0000000        
D   1
 1      0.8000000              1.0000000

HYDROGEN
S   3
 1     18.7311370              0.03349460      
 2      2.8253937              0.23472695      
 3      0.6401217              0.81375733      
S   1
 1      0.1612778              1.0000000        
S   1
 1      0.0360000              1.0000000        
P   1
 1      1.1000000              1.0000000

Note that the new carbon basis set has no diffuse L (sp) shell with the exponent of 0.0438000, while the new hydrogen basis set has two additional shells, diffuse s with the exponent of 0.0360000 and polarization p with the exponent of 1.1000000.

So, try to change both $CONTRL group and basis sets.