Depending on how bad it is…I’d run a motor flush through the engine every 2k miles and change with fresh oil and filter. Do that 3-4 times and see how it does.
As others pointed out…if it’s really bad doing a flush can cause large chunks of sludge to be lodged in the oil pickup screen that will STOP oil flow.
One old timer (older then me) had a solution. Drain the oil…put the plug back in…the add about 3 gallons of Kerosene (which Gunk is anyways). Let it sit for a couple of hours (DO NOT START THE ENGINE). Drain and then refill with good clean oil and new filter. I never tried this method.
MikeInNH I had a old timer tell me almost the same thing. What I was told and did this on 350 Skylark I had. You put 2 gallons of kerosene in after you drain the oil. Then remove the spark plugs. Crank the motor for 1 min wait 2 min then crank 1. Do this a few time then drain. Fill with oil run till good and warm. Then drain oil and refill and change after 1000 miles. All should be good. It worked for me. Would I do it on a car today? No. Well maybe a V8 chevy but not something like the OP car. I would think it would damage it.
I think your plan on using Auto-RX is a good one. While I haven’t used it myself since I haven’t needed it I think you will be happy with the results. If I did have this kind of problem it would be my first choice to use. Many folks here don’t like the product saying it is basically ‘snake oil’ but I don’t think any have tried it and checked it out for themselves. It would be great if you let us know what you think of the product after you have finished the process so please keep us posted on the results. Weather you like, or dislike the product, it would be good to have some direct feedback from someone who has tried the product to pass on to someone else who has the same trouble in the future.
With testimonials about how this stuff works so good that it turned the oil black in a brand new engine makes me agree that it is total crap and I would not use it.