IMO very likely not a GTIA problem.
Boulder Dash it appears doesn't use PM graphics, so those glitches with Rockford are actully character stores gone awry.
The game uses 80 bytes of seperation betwen each character line so the "half Rockford" under and to the left is either 154 or 158 characters ahead of where it should be (can't work out who's the proper Rockford).
That doesn't really correlate to something like a sticking address bit which would usually give an offset of a power of 2.
It's hard to say what's going wrong - it might just be memory corruption causing the program to be altered. Might be something else.
Maybe try something like this in Basic. Then give it the same 30-40 minutes:
10 GR. 8 : SE. 2,0,0
20 C = NOT C : C. C
30 F. Y = 0 TO 191 : F. X=0 TO 319 : PLOT X,Y : N.X : N.Y
40 GOTO 20
That'll slowly fill the screen with solid colour then back to blank. But it's doing a bit of variable memory access so might be able to reproduce the problem.
Note that 6502 is never really in a halted state - it accesses memory on practically every cycle (ignoring WSYNC and DMA states) so an inactive system isn't really like that but generally the variation of memory accesses will be less.