Here's more or less the parts for what I would build...
Clevite Engine Parts CB831P - Clevite P-Series Rod Bearings - $55.76
Clevite Engine Parts MS1432P - Clevite P-Series Main Bearings - $52.97
Clevite Engine Parts SH510S - Clevite Camshaft Bearings - $25.97
Fel-Pro 17360 - Fel-Pro Performance Marine Intake Gaskets - $24.97
Fel-Pro VS50068R - Fel-Pro PermaDry Valve Cover Gaskets - $10.97
Ford Performance Racing Parts M-6051-CP331 - Ford Racing Performance Cylinder Head Gaskets - $76.97
Ford Performance Racing Parts M-6710-A351 - Ford Racing Oil Pan Gaskets - $22.97
JE Pistons S100S8-40305 - JE Pistons Pro Seal Premium Sportsman Series Piston Rings - $99.46
Melling IS-83 - Melling Heavy-Duty Intermediate Driveshafts - $12.97
Melling M83 - Melling Oil Pumps - $41.97
Sportsman Racing Products 149606-8 - SRP Ford Small Block Dish Top Pistons - $619.68
Trick Flow Specialties TFS-51400510 - Trick Flow® Roller Rocker Arms - $289.97
Trick Flow Specialties TFS-51410002-M61 - Trick Flow® Twisted Wedge® 170 Cylinder Heads for Small Block Ford - $1,125.00
Part Subtotal $2,459.63
You'll be + $200 for cam and lifters, and about another $100-$200 for pushrods, gaskets, misc bits. Machine work pricing is highly variable depending on region, as well as what your engine needs. $500-$1000 is my guess. So $3500-$4000 to do it with nice heads. Can probably shave about $500 cutting corners on parts, but I would want to build a solid bottom end as top priority as top end is quicker and easier to change is desired.
Anyhow... Some numbers for power and compression with two different cams and zero deck vs .013 in the hole.
Comp XE 262/270 .013" piston to deck
Comp XE 262/270 zero deck
Comp XE 256/262 .013" piston to deck
Comp XE 256/262 zero deck
The 262/270 is about as big a cam as I'd go for a towboat with stock manifolds and displacement. Idle will be slightly higher than stock and slightly noticeable but should not be too obnoxious in a 351w. The 35-235-3 XE 4x4 cam is interesting too Sacrifices some top end HP but more HP at lower RPM and slightly flatter torque curve.
Comp has some "marine" grinds there's not split duration. Simple old style cams. The 31-216-2 is a 260/260 and compares to the XE256/270 but leaves at least 10 hp and ft/lbs on the table at all RPM and doesn't have quite the potential when uncorking the exhaust. The 31-218-2 is a 268/268. I'd expect it to maybe have a slightly rougher idle than the XE 262/270 as it has more overlap. HP is similar at peak but less at lower RPM and it's down a bit on torque from the XE split duration cams. Didn't run dynamic numbers on any of those.
Personally I'd be tempted to run the XE 256/262
Note that exhaust is the biggest restriction. I put HP manifolds in as marine pyramid exhaust flow better than logs, but a far cry from a true performance manifold or header. Changing exhaust to headers in DD is 50+ HP more with pretty much any cam.
What heads do you currently have? To get the price tag down under budget the heads are not an option. Heads and associated costs are adding about $1500 to the price tag. Machine work on your heads (cut seats, new guides, new valves if/where needed, surface if needed) I would expect to be in the $500-$700 range. Also figure on +$100 for valve springs for the cam vs the already assembled heads.
Let me know what your head castings are and if I can find flow numbers I can see what they will do. I'll also see about checking GT40 and GT40p heads.