Trans has to come out! Or the engine! YOUR CHOICE!
You have to remove the crank to do all the bearings properly.

I had one do this once years ago, and if Im not mistaken there is a spring that determines pressure in the pump that got weak and was replaced. Also fill the cavity of the pump with vasoline so it prime on start up. anyway, it may be worth looking at before yanking the engine. 120000 miles should not mean death on the bottem end unless the motor was abused.

If the tolerances are starting to open up, it will need more VOLUME to stay alive. Heavy oil may help a bit, but like 3800 said your only delaying the inevitable. Have the PUMP gears, spring, ectc... checked first. It may be a simple priming problem . :?

You're thinking of the older 3800'*. The 92-95 Series I just use a gear inside a race. The two parts are machine to a certain tolerance. Short lived engines are all caused by abase either. Mine died early because of a faulty oil filter. Most die early due to coolant getting into the bearing races & eating the bearings away.

if it was me, and the oil pressure was in fact near zero, I'd take off the pan, replace the main and rod bearings (with 0.001 unders which should be available, they are for a lot of engines), and throw in an oil pump. Its a $125 gamble, but I'd take it.

At least its not an LA-series small-block mopar that'* known for main bearing issues, where the oil pressure goes up when you coast downhill......

I have not done this on a 3800 but I have rebuilt lower ends on other vehicles without pulling the engines. I rebuilt the lower end on my Dodge P/U because of the same symptons. I used stock bearings because as long as the crank journals are not damaged it should be virtually the same diameter. The babbit material of the bearing is very soft (it is tin based) and does not come into contact with the journal because of the hydrodynamic wedge created by the oil.
I pulled the oil pan and took off a connecting rod end cap and journal bearing cap to inspect the bearings. The babbit material was pretty much wiped but the crank was still in good shape. From there I took off all the rest of the caps and to remove the top half of the bearings I used a flat piece of flexible plastic and tapped it up through the top of the rods and journals to spin the top half of the bearings around.
I was able to get a high volume oil pump for the truck but from what was said earlier, that may not be an option of the 3800. The assembly is opposite to disassembly and the only one that is difficult is the front because of the timing chain and the front cover. I simply had a buddy pull down on the balancer (he was over 200lbs) which gave the clearance I needed to tap the bearing in place. I plasti-gauged the assembly to check clearance and all was great.
To start it up I removed the coil wire and cranked until I got some oil pressure (I oiled the bearings during assemble...). I had the truck for about another 100,000kms before giving it back to my father and then it ended up going to my brother. He eventually got rid of it.

Now, this does not fix the camshaft bearings which could be a source of pressure loss. The whole job took me about 4 hrs but that was at the college with a hoist and every tool available.

Either way you look at it, the oil pan has got to come off and from there it is just a couple of minutes to remove an end cap to inspect the bearing.

This is not a beginner job but it is possible and of course does not replace a full engine rebuild.

Just though I would give you something to think about.

Camshaft bearings going in a 3800 are as rare as "Hen'* Teeth"!

I've personally seen more crankshaft bearings (normally the #1 & #6 bearings) go on a 3800 in the last year than most will see in a lifetime, while working at a GM Dealership. My OWN 92 SE being one of these very probmatic 3800 engines too. If you're looking to "dump" the car then you can do this:

Drain off about 1.5L of oil & replace it with 20W50 oil or 80W90 Gear Oil. This will increase the oil pressure enough to keep it out of the "Red Zone" & will stop the alarm from sounding when the car idles.

This will not solve the problem though & a good mechanic will still notice the low oil pressure! I did this to mine, but still told them that the oil pressure was low & should be looked into further. I also knocked off $3000 off the price of the car (this is what the engine job would roughly cost).