Running wire through ceiling, ceiling joists blocking access to the top of the frame
A doubled joist is 3" wide.

A standard 2x4 is 3.5" wide.  

You have a lip on one edge or the other.

Can you not start your hole on this lip taking perhaps a nibble out of the corner of the joist?



Joists support.  If this double joist has a wall under it, what is it supporting that the wall itself isn't sufficient.

In normal configuration the bottom of a joist is in tension, while the top is in compression.  This assumes that it's being supported at the ends.  Gets more complicated when it's supported at multiple points.

Taking a chunk out of the bottom, where it is already resting on the wall below isn't going to make the building collapse.  Because of that wall, there is no tension on the bottom of the joist.