I spent a whole day photographing there on an overcast day last October. I just checked through my settings. ISO 1600, f4-f9.5 with probably f8 being the commonest; 1/15 handheld with IS. Even at these settings I'm exposing dark rather than light. The issue isn't helped by the fact that to get other than bland wide-angle shots you need a longish lens and so depth of field isn't something that you can forget about. I was using pretty much the same settings in pit 1- where the volume is- and in the glass cases/other pits.
Based on this I couldn't possibly suggest that you will be OK with ISO400 film. You either need something faster or hope for more ambient light getting into the pits. I did see a Chinese guy photographing with a tripod but it was quite a quiet day, and for all I know he got pounced upon by the guards right after I saw him. Probably wouldn't be physically tenable on a busy day anyway.