Compression is 180, 200, 240
The good news is your Universal is a marinized Kubota D950. Look at the dipstick for the Kubota numbers. With that you can buy Kubota parts at farm or lawn equipment dealers for about a third of what Westerbeke charges.
The compression spec on this engine is 448 psi new with an allowable lower limit of 337 psi and a variation of no more than 10% between cylinders. You're well below that.
Your white smoke is unburnt fuel from low compression. Hard starting and poor running when cold are other results.
White smoke can also be caused by coolant leaking into the engine. That can't be ruled out, but fixing the compression problem will fix any coolant leakage problem.
Some a$$hole mechanics will not open the throttle wich will cause low readings.
A mechanic who compression tests a diesel with the throttle open has no idea what he's doing.
This engine is a diesel. It has no throttle valve in the intake. Throttle position will have no effect whatsoever on compression readings. Depending on the fuel pump arrangement, if there is no fuel shut off solenoid the throttle is used to shut off fuel to the engine. If the throttle isn't in the shut off position when a compression test is run, the engine will try to start. Since the compression gauge is most likely installed in a glow plug hole, if that cylinder fires the compression gauge will be blown up.
So if you see a "mechanic" try to compression test a diesel with the throttle open, fire him before he hurts himself on your boat.
From your description this engine has been badly neglected. Since the anode in the heat exchanger was gone, there's probably a bunch of corrosion plugging things up and causing the overheating. Sounds like your exhaust system is a bunch of mismatched pieces kludged together.
Since the compression is so low our mechanic wants to do a full rebuild.
There is something called a cylinder leak down tester that's used to pinpoint where the compression is being lost.:
They're $30 at Harbor Freight, but you'll probably also need their $25 diesel compression gauge to get the fitting for the glow plug holes.
If you onlly need a valve job, just the head can be pulled and sent out. With the engine open you can decide if a full rebuild is necessary. If the rings are the problem, the engine has to come out and you might as well rebuild the whole thing then.
As a stopgap measure we were thinking of replacing the heat exchanger: $650.
Do you know it's bad and can't be repaired? Better to pull it apart, clean it and see where you are before replacing it.
Replace filter: $315
Absolutely replace the filter. But rather than a "marine" unit, I'd look at industrial models. For instance, Northern Tool sells Goldenrod Water-Block Fuel Filter
for $37, with $12 replacement cartridges:
Rebuild injectors: $285
Do you know something is wrong with them?
While you're replacing stuff, take the whole exhaust system apart, throw away anything that's bad, and rebuild it with good parts. Use double hose clamps and not glue for putting things together.
Do you think that we can get another season or two out of this engine?
Once the problems are fixed, and provided it's maintained, it'll last decades.