Moving main service breaker panel lower on wall exposes feeder wires non-sheathed
Can't do it. There must be at least 1/4" of sheath past the cable clamp.  No cable clamp. 

Also there are painful limits on number of jacketed Romex cables in conduit. You can't just cram 'em in. 

Only if you put a junction box at the top of the conduit

Fit a junction box there, then use a less-than-2-foot run of conduit called a "nipple".  

Consolidate all the grounds into a single ground wire (of the largest size) that you carry through the conduit.  If you use steel boxes and EMT conduit (if indoors) or Rigid conduit (if outdoors), then the conduit itself carries the ground, and you can terminate at the junction box itself (get a box with a raised nub for the ground screw). 

Given that all your cables are 14/2, each cable splice takes 8 cubic inches (2" x 4 wires), and you lose another 4 cubic inches for all cable clamps and all grounds.  That means: 


A 4" square box takes 2 splices
A 4-11/16" square box takes 4 splices
A 6"x2" box takes 8 splices
A 6"x4" box takes 17 splices


"But I'm not splicing! I'm rolling the individual Romex conductors right on through to the panel!"  Yeah, that's not allowed by Code because those individual wires are not rated for conduit use.  You're meant to splice to another wire type (THHN).  I don't seriously expect you to do that... however I want to make sure you already have the cubic inches in the junction box, in case you get flagged and are forced to do them.  If you don't have to replace the junction box, then you could do it one pair at a time and not get too confused.  Otherwise, what a mess! 

One thing you really must do, in any case, is bundle/group your wire pairs/triples.  You can't simply have a spew of blacks and a spew of whites raining down from the conduits.  You have to mark, in the main panel, which hots go to which neutral.   That's as easy as wrapping the pair/triplet with electrical tape positioned so it'll be visible in the main panel.  

As mentioned, grounds can be consolidated in the junction box to a single wire (of the largest size), and if metal, can simply be pigtailed to the box itself. 

This may be moot, though.  Outside may be mandatory

The upcoming NEC, 2020, has only been adopted by one state (Mass.) AFAIK. Once your state adopts it, you must put the disconnect outdoors.  Mind you, all the existing houses are grandfathered, and aren't required to retrofit a disconnect... but even under grandfathering, any step must be in the right direction.  Once NEC 2020 is adopted in your state, the disconnect will have to be outside.  Word to the wise: get that permit pulled soon if you want it indoors.