Dry exhaust to wet exhaust

Why did the factory then not go straight down thru the bottom?

If the OP has an 8" hole cut through the bottom outboard with a FRP prepared flange inside and a 3" waterline bypass this installation will be relatively simple as exhaust retrofits go. I would still recommend a 36"vertical wet muffler in line to silence the bypass and I would go with a dry riser and spray ring 2ft. before the muffler . This is a reasonably simple retrofit and can be done on the cheap if the OP is handy and picks his subs wisely. Detroit's sound like Sherman tanks without resonators even when muffled through underwater discharges.

The dive boat with the side exhaust is using 30 old technology with a horizontal dry muffler that has two ft. thickness of rocks wool insulation/ lagging around the dry can for thermal isolation from the structure and radiant heat in the E.R & the sea water is injected down line from the muffler in this system. Your vessel is a great candidate for a simple underwater / bypass wet exhaust system to free up the space in the salon/ galley area. A new wet exhaust muffler / resonator can be vertically or horizontally mounted outboard in the machinery space & doesn't require lagging after the water injection point and it will be a small foot print due to the size of your motors. Your stepping outside of the box in your thought process of what's new (expensive and unproven) technology like ceramics and high tech insulation materials. This vessel has a max price/ investment point and your best to keep it simple. A wet exhaust muffler for your rated HP and back pressure specifications would be small compared to the ancient dry system on the dive boat. Call a good marine exhaust fabricator in your area and have them give you a few different scenarios to move fwd. with and then either accept a proposal from them or price the system out for yourself and use good subs to complete the process.

From your photos my statements are an educated guess at best. (SWAG) I see a large diameter Blue silicone hose all the way aft that looks to be close to the inlet of the muffler and that would lead me to believe the system would be wet but the lagging on the can says "dry" to me. The photo of the vessel on anchor has a waterline exhaust discharge fwd. just under or aft of the pilot house door so the discharge of this muffler is facing fwd and that would add to back pressure issues if this were a wet system. The forward facing outlet discharge on this system is an anomaly for the running angle of any vessel. Call a marine exhaust company in your area and have them give you a few good options for this vessel.

I assume your picture is similar to a resonator you are talking about. Designed above my pay grade.
However, I have been on many older boats (glass & alloy) with 3412s, 3208s, 71 & 92s that at or just after the down turn of the dry exhaust, use a dump can to mix and cool the exhaust gasses with raw water, then thru some humped hoses, straight into a near vertical pipe fastened to the bottom of the hull. The larger engines with a smaller pipe out the sides or the stern.
On the 1400HP 3412s, I replaced the hoses and there were no baffles in the vertical tube, just the eire light from out side the boat in the water coming up. I thought the 3412s were the quietest (80 Nova tech) boat I was ever on.

I like tanks. My youngest kat is "Sherman M4A2 Tank" (conjoined 6-71s).

Quiet as a church mouse.

My Tiger tank pounds the deck over head in the night.