Relief valve hanging open, and hardening of the oil pickup oring are documented events on the LS series

I'd probably have a mechanical gauge on it that I could see while driving it around......and one eye on the gauge the whole time 

Why does it take 20 to 30 minutes for any of the things mentioned to suddenly cause a problem

I think somebody's jumping to some conclusions unless there's more info than what's given here.

Example I saw yesterday, I have a 2003 Yukon with this same basic engine structure,  This Yukon has always had 40 PSI or better at idle and 60 PSI at any RPM over 2,000.  Pretty normal.

I towed the Cobalt I have been working on 500 miles one way yesterday to its new home.  Went over several mountain passes 4,000 to 7,000 ft elevation.  The boat and trailer were 6,000 pounds.  It was 100* out.   At first I had my normal 60 PSI on the highway, I was driving in 3rd gear, avoiding overdrive with this load.  After about one hour oil pressure dropped to 40 PSI, did not go lower except at idle.   I was wishing I had an Oil Cooler on this engine.   The heat and constant hard work dropped my oil pressure.   The last leg of this trip over 20 miles I went from about 2,000 ft to 7,000 ft climbing a very steep, very winding road.  The Yukon was in 1st gear taching 4,000 RPM for about a half hour.  Made me nervous but it seems fine today.  I was going all of 25-30 mph and could not go faster, it was horribly steep with that load.

I have had the pan off the newer LS engines and there is a bypass built in to limit oil pressure.  This was installed to avoid damage to the Cylinder Deactivation lifters used on some engines.  Those systems can fail due to high oil pressure.  Your boat will not have this option and the Pressure relief can be eliminated/removed/plugged.  I have done this to a 2008 LS engine, you have to remove the pan to do that work.   The Oil Pick Up O'Ring is a real problem in passenger cars and trucks, they get stiff and quit sealing.  It is a $4 part and if you pull the pan change it so you don't have to worry.  I would not think a boat would have the problem with that Oring due to lower heat and far less use than a passenger car or truck.

Most tell you to change the oil pump.  Oil Pumps are the best oiled part inside the engine, they get oil first always.  Due to that they have less wear than most any part in that engine.  What does happen is some particle can get stuck in the by pass keeping it from working properly.  You can take it apart and clean it, add a shim if you wish for more pressure.

If I had to guess which one is your problem I would lean towards the secondary bypass which is built into the pan, not into the oil pump but you may find out the secondary bypass was eliminated by the engine manufacturer since cylinder de activation is not used in boats.  The 2008 LS 5.3L engine I worked on was reading zero oil pressure when I got it.  Pulling the pan and blocking off the secondary relief, plus a new O'ring, had that car at a solid 50 PSI at idle with the same oil pump.

Before doing any of this you would want to verify you have an issue and not just a bad Oil Pressure sender.

You might figure out that AFM/cylinder deactivation didn't exist on a 2004 Chevy LS engine so some of the above doesn't pertain 

Most important sentence is his last one.............verify the issue before jumping to conclusions

On the GM LS engines if you replace the Oil Pick up tube Oring, be very careful to match up to what you already have.  GM used 2 designs I know of.  I think they color code, Red and Green, there might be a black option also, but match the size.  Melling Oil Pump company sells the Orings, so does Fel Pro or the dealer if it comes to that.