Shovelbill makes some good points, but stating anything about buying a Dodge on this forum... ."GASP!" (LOL, My buddy built a nice 2wd 89 Dodge with the Magnum 5.9L 360, nice power over the original 360, but it'll couldnt haul 10,000lbs over an ant hill in a stiff breeze.
That said;
10K is A LOT of Weight for any pickup originally rated under 1 Ton, but if yours is already an 8 lug 2500HD, as said above, you have a lot of the parts already needed to get there.
(FYI, If its a 6 lug, you dont have a HD 2500). At minimum, I strongly recommend going to a Full Float 14 Bolt, 4.10's, and Duallies for that kind of weight on the back of any GM truck. A Semi-Float 14 Bolt is a damn good axle, but its a Medium Duty GM Truck Axle. Its 9.5" ring gear and C-Clips will definately fail under that kind of weight torture...
Find a C3500 Dually, grab the rear leafs, axle, rear wheels, rear wheel flares, and pick off any bits you'll need for an engine swap to a 454 or 502, because the 350 wont live very long towing +10K lbs
That is well-beyond the capabilities of any relatively-stock SBC.... especially a late-80's, thin-cast, smogger-block 350. Im sure people will chime in that you could do it, but as us New Englanders say; "You cahnt get thah from he-ah". Realistically, you really cant, not without stripping it down to a bare block, & spending a pile of cash, for a less than spectacular result... Dont get me wrong, I love the SBC 350, but to make that engine pull that much happily, you'd be spending about $1000 per 1000lbs to get it to be where you want it, and itd run hotter than Obama's temper watching Trump bulldoze the "Legacy".
As you seem to already know, the 2500 came in 2 flavors,
"Light Duty 2500": really just a 1/2 Ton with some beefier parts.
"Heavy 2500", Full 3/4 Ton shared some 1 Ton parts.
Here's some info that I recall from my own experiences, (these were trucks I drove for a friend/employer):
1994 C3500 (2WD), Reg Cab/ Longbed, 7.4L (TBI 454), TH400, & 4.10:1 Dually Axle 5th Wheel had a towing capacity max GVWR of about 9000lbs.
1997 C3500 (2WD), Reg Cab/ Longbed, 7.4L (Vortec 454), 4L80E, & 4.10:1 Dually Axle 5th Wheel had a towing capacity max GVWR of about 10,000lbs.
Both were Very Reliable, but the '94 TBI 454 was pretty doggy towing uphill... a Q-Jet, aluminum intake, headers, dual exhaust, a real cam profile, & some good heads, would have been MUCH better for power and mileage... (Im not a fan of TBI anyway). The '97 was noticably more responsive to the throttle, better on mileage, and wasnt as quick to start lugging up a hill... but it felt like it needed a better exhaust system and cam profile to capitalize on its power. I know the '96-'00 454's Vortec heads, much like the L31 Vortec 350 heads, were a big improvement over the 80's "swirl ports". IIRC, the crate 502 uses the same/similar Vortec head design as the stock Vortec 454. Having direct injection is another huge step up from the TBI... More reliable & excellent fuel ratio, vs the TBI's unequal, rich-to-lean fuel distribution amongst all 8 cylinders. Certainly a 3" dual exhaust, headers, and healthy cam profile (502 cam?), would give it a nice bump in power. I recall quite a few guys liking the Vortec 454 in its day. The 4L80E did need a rebuild around 120K... (4L80E is essentially a modified TH400 w/ an Overdrive Gear & electronics).
Essentially, what Ive written above is a more complicated way of saying, you cant get that out of your truck for $2500.