Question: Was your old 3406B using a JWAC (jacket water aftercooler)?

I assume the newer (1992) 3406C model, was pulled out of a semi-truck and thus it uses ATAAC (air-to-air Aftercooler).

If the 310 HP engine, was a semi-truck engine, then the serial number probably starts with "3ZJ"

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The 310 HP, looks like 3ZJ21620, would be my guess.

I see the old engine was 24.0 degree BTDC timing; but my guess is the 310 HP engine is probably 18.0 degree BTDC . Fuel injection pump won't swap, that for sure = probably different compression ratio and pistons and nozzles, etc.

Did the guys, that removed old 310 HP engine cover or tape the intake ports? (= real easy for parts, washers, nuts to fall inside the engine, if people aren't careful about this stuff {remember, those guys probably didn't care about "that" engine, during removal, so they might have been somewhat careless, about any debris falling into cylinder head intake ports})

How many miles, on old 310 HP engine?

 Time for engine bearing replacement ?

I would be worried about your old 360 HP turbo, because you had "metal in the oil" during that failure. (= metal debris might have gotten into turbo's bearings)

I'm just guessing, but I assume the easiest, cheapest option, would be to swap over JWAC components to 310 engine, buy reman turbo cartridge(center part of turbo) for a 360 HP engine, and install on that the 310 engine (may have to double check if exhaust manifold would be also be required during swap (whether a different part number or not); then finally just have someone turn the fuel screws, on the 310 HP engine's governor up to around 360 HP's fuel delivery amount. {this method, isn't "by the book", but you didn't want to throw a bunch of money into this unit, either}

The crankshaft is different, on the 1992 "3ZJ"  (310 HP) engine = better = it will have the "wider" rod journals.(thus connecting rods are different, also; and probably piston spray tubes, too) 

Note: The rod and main bearings "should be" good for 500,000 miles of regular "over-the-road" driving. (this is for the wider rod journal crankshafts, only)

I disagree with BOTH these statements = there is too much difference in TIMING !!!

You go mixing and mis-matching parts like that, and you will end up with piston failures that will look like this:

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I thought of something else, because you mentioned 310 HP economy, I believe that governor might be set to an 310 HP @ 1800 rpm rating.

 Your old engine was a 2100 rpm rating, so if a person used the 310 engine and governor, you would probably need a 2100 rpm governor spring (inexpensive) inside that governor, too.

I'll tell you a story, and I'm friends with the CAT foreman in Omaha, and about 10-12 years ago, he mentioned that some truckers with older electronic engines(PEEC) set at 310 HP, were going to truck wrecking yards and buying used 400 HP ECMs (engine computers) and bolting them up to their 310 HP engines, and not changing anything else. He said the little 310 HP turbos lasted, quite a while (= actually spinning too fast), then when they did fail, the truckers would have it replaced with a 400 HP turbo part number, at that moment.

 I assume some of the other 310 HP parts probably weren't correct for 400 HP either, but according to him, they must be holding together with the amount of fuel going thru a 400 HP engine. 

I mention this because you might be getting "overly worried" about getting these engines set up, to CAT specs, that CAT had to use to pass emissions and get decent fuel economy numbers, BUT it doesn't mean some of these "matched components"(inside engine) can't handle some more HP, without engine damage.  

For me, I might be more interested in, what is the most inexpensive way, to get that "3ZJ" engine up to 350, 400 or 425 HP rating at 2100 rpm. {Meaning, which one of those 3 "CAT Factory" choices, used the same pistons, engine camshaft, and fuel injection pump camshaft as your 310 HP economy engine uses and the SAME base Timing spec. (big ticket items;$$$)}

 After that, then you look at fuel nozzle part number differences and turbo part number differences (= these are cheaper and easier to change).

I'm pretty sure you will automatically need to change, items such as Governor Spring(for 2100); timing advance spring (maybe), Torque spring and shims (inside governor, cheap); and reset fuel settings, for roughly 360 - 400 HP.

Honestly, the very cheapest route; is to just install a 2100 rpm governor spring, turn the two fuel screws out another 1.5 turns each, and set "high idle" (top engine rpms) to 2300 rpms, on the newer "3ZJ" 310 HP engine. (At least you know all the components, inside that engine, match for a 310 HP configuration)