Electrical box caught on fire

I have a rule: Nobody does things for no reason. 600A is a crazy amount of service, and if the reason for it isn't obvious, figure it out before you change anything. Once you understand that...

Your principle of feeding one subpanel off another has merit. However you must bridge over all the wires together - two hots, neutral and ground. You never pull over a hot and have its partner wires return via a different route, For a variety of reasons. This means if one wire in a cable run is dead, the whole cable run is useless and must be taken out of service entirely.

But I wouldn't focus on the cross-connection yet. I'd try to save this setup. I'm betting it's a termination problem not yet found - it's unusual for wires to just fail.

The bigger problem is: This work was all installed at once, right? Whatever damaged one thing could well be damaging others. Did you find corrosion on the connections you serviced? They're all that way. Don't wait til they fail, because a neutral failing is especially bad news.

As a temporary workaround, like, to get you to the weekend when you can fix this, you might move your 120V loads to the breaker spaces that are working. If you need more breakers, either share breakers (when legal) or buy duplex breakers.

I find almost all such problems are with terminations, perhaps in a splice box you haven't found yet. Don't just tighten lugs, de-energize it and take it all apart and really give it a once-over and fastidious cleaning. If it's aluminum wire (AA-8000-series is legal and OK), apply the anti-oxidation goop. Only then, look at the cable itself.

Somebody who puts in 600A service doesn't cheap out on the installation. There's a good chance your cable run is in conduit, which is designed to make cable replacement easy. On the other hand, it surprises me that cable would fail in conduit, so I'd be concerned maybe something penetrated the conduit, damaging both conduit and wire. Any wire damage seems vanishingly unlikely under a foundation, far more likely in a more accessible place (perhaps a recently accessed place - had any diggers around lately?)

And by the way, it's possible to splice underground direct-burial cable.

If the cable is in conduit, easily replacing wire is the whole point of conduit. They spent extra money as insurance for this situation - use it! Validate that the conduit is physically intact (not collapsed). The techy way is to energize the bad wire (only) and use a detector to find the wire break (by looking for EMFs). That tells you how far down to send a borescope (a plumber will have that if an electrician doesn't).

A low-tech way to inspect conduit is to disconnect the wire bundle at both ends and pull it an inch and see if it gives more than the normal resistance. The "Alexander the Great"** method is to pull the entire bundle, inspect, maybe borescope, fish and pull it back in, and see what happens. Mind you, this is not to continue the old wire bundle in service - but merely to use it as a "test dummy" to test whether the conduit is pullable. If there are any defects in the wire, replace all of them unless it is extremely clear what went wrong.

If the conduit is intact and the wire is bad, this is routine: pull and replace the wires. That job is easier with specialized tools an electrician will have those on his truck.

Wires don't just randomly fail in conduit. This for sure: whatever killed the one phase threatens the others. You'll want to know what that is.

I'd use a flush mount NEMA 1 pull box and mechanical setscrew/splice connectors

While an ordinary junction box is simply too small for splicing 4AWG conductors, larger boxes are available. These are called pull boxes or NEMA enclosures, and in particular, you need a flush mount (into the ceiling), NEMA 1 (indoor) box. Size-wise, you are looking at a minimum dimension of 6" across as a 4/4/4/6 or 4/4/4/4 SER cable will fit into a 1" conduit of the appropriate type (nobody uses Type A PVC conduit, but it provides the most fill area/diameter of any conduit type in the Code, so its what's used when transposing cable sizes into conduit sizes for this) and NEC 314.28(A)(2) requires the box to be at least six times as long as the largest conduit entry into it, more or less:

(2) Angle or U Pulls, or Splices. Where splices or where angle or U pulls are made, the distance between each raceway entry inside the box or conduit body and the opposite wall of the box or conduit body shall not be less than six times the metric designator (trade size) of the largest raceway in a row. This distance shall be increased for additional entries by the amount of the sum of the diameters of all other raceway entries in the same row on the same wall of the box. Each row shall be calculated individually, and the single row that provides the maximum distance shall be used.

Exception: Where a raceway or cable entry is in the wall of a box or conduit body opposite a removable cover, the distance from that wall to the cover shall be permitted to comply with the distance required for one wire per terminal in Table 312.6(A).

The distance between raceway entries enclosing the same conductor shall not be less than six times the metric designator (trade size) of the larger raceway.

When transposing cable size into raceway size in 314.28(A)(1) and (A)(2), the minimum metric designator (trade size) raceway required for the number and size of conductors in the cable shall be used.

Inside this box, the actual wire splicing is performed using appropriately sized mechanical splice connectors ("Polaris" or "Unitap" are common trade names for them) for the hots and neutral, and a small equipment grounding bar for the ground wires -- this ground bar screws into a pre-tapped hole for such on the back of the box using a 10-32 machine screw. All of these connections will need to be torqued to manufacturer specification using an inch-pound torque wrench or torque screwdriver, by the way.

As to mounting the box, you'll want to use a piece or two of scrap 1x or electrical strut ("unistrut") as crossmembers between the joists to mount the box to, given that your average NEMA 1 box is designed to be mounted through the back, not a side. You'll need to screw it to the crossmembers with the appropriate screw for the crossmembers you're using, too -- NEMA boxes are not designed to be nailed to things.

The RV outlet is a subpanel

The good news is that the RV outlet assembly is a subpanel, so provided you use appropriately sized cable (6/3 copper NM is fine here provided physical damage is of no concern), it's no different than any other situation where you have two subpanels on the same feeder. The "feeder tap" rules in NEC 240.24 do not apply here, by the way, since the conductors from the splice point to the RV outlet assembly are sized for the full 50A the breaker in the main panel will allow.

(As a sidenote, this logic does not apply to a simple receptacle -- the use of a plain receptacle here would result in a mix of utilization devices and subpanels on the same circuit section, which is something that the NEC does not appear to contemplate.)