Fridge leaking - condensation

[conj]

Looking for some expert advice please -
I have an aft fridge in the cockpit of our boat. Our cabin is directly adjacent but below but most of the base fridge area is above our legs when in bed.
When the fridge is run for a while, water starts to drip onto our bed...I thought it was a rain leak but have confirmed it only happens when the fridge has been running.
Our boat is a 1980 Pan Oceanic. My theory is that the insulation around the fridge is getting saturated with condensation and eventually seeping through the timbers onto our bed. I cannot see any other signs of leakage.
Taking all this apart to see is a major task so I am thinking of maybe refitting new closed foam cell around the inside of the fridge area to try and prevent the condensation forming...as I'm guessing the old stuff in there wasn't the best performing insulant.
I have attached a pic of the unit.
Would appreciate some ideas or opinions.
Thanks

[GordMay]

Do you have a condensate pan, and drain tube, at the bottom of your refrigerator?
If your drain hose is blocked [or you don’t have one], condensate water may collect in the pan, faster than it can evapourate, until it overflows.

Condensation inside a refrigerator is generally normal, and is caused by the cooling process. As the fridge cools, the air inside becomes cooler, and can no longer hold as much moisture. The excess moisture then condenses, on the interior walls of the fridge, and runs down, into the drip pan.

Water will condense, and collect, at the coldest point.
Cold air can hold less moisture than warm air.
Warm air outside the refrigerator can absorb more moisture, than the cold air inside the refrigerator.
In refrigerators, water condenses on the rear interior wall, because this is where the evaporator, which extracts the warmth from the interior, is located.

This can be exacerbated by various factors, like faulty door seals [1], humid produce [2], overcrowding in the fridge [3], high surrounding [ambient] temperatures [4], or low thermostat settings [5].

[1] If the door gasket is damaged, torn, or missing, it can allow warm air to enter the fridge, and cause condensation on the interior walls.

[2] Produce or other foods made mostly of water, such as meat and dairy products, can create condensation inside a fridge by releasing moisture into the air. Storing dishes that are still warm inside a fridge can also release moisture. The moisture from these items will condense on the coldest part of the fridge, the rear wall, as condensation. Until the temperature inside the fridge stabilizes again, the condensation will remain. Store produce in sealed containers or plastic bags, or wipe them down with a dry cloth, before storing them in the fridge.

[3] When the fridge is packed too tightly, cold air inside can’t circulate properly. This causes warmer temperatures, and increased humidity, which leads to condensation.

[4] High ambient temperatures can cause the compressor to run for longer to maintain the temperature inside the fridge, which can cause condensation, and sometimes ice formation.

[5] A thermostat set too low can increase moisture towards the rear wall inside the fridge, which is the coldest part of the ridge. Additionally, a low temperature can cause the compressor to run longer, leaving less time for condensation to drain. About 37°F is an ideal temperature for a refrigerator to be set at; however, you should refer to your Owner’s Manual for the temperature recommended for your fridge.

[conj]

Thanks GordMay,
A lot of very interesting info. One thing of concern. There is no drain hole at the bottom. Sounds like I should install one.
The lid doesn't seal 100% as I have replaced all seals but the nature of the setup, the lid doesn't sit flat.