NEC, use more extension boxes or an access panel?
Yes J boxes can be behind access panels as long as they meet the code's definition of accessible .I would not add to that mess if you can't re work the conduits and re pull the wire as all ready suggested make sure that your access panel meets fire code. If I was going to deal with that and didn't have the means or budget to re do the grc using an access panel. I'd take that apart down to one extension ring and mount a 4 and 11/16 box maybe on the beam to the right or to the left if there is something reasonable to fasten it to (left would make it easier to rework the emt) run flex or emt to your new box from the extension or if there is a Ko available in the original box. Connect the existing flex and emt to the new box. Then work from that box to the one you need in the ceiling. You may need a larger box than a 4 and 11 that will be dependent on how many wires need to be spliced or run through that box.