Can I adjust away a creak from a bottom bracket?

I've had an irritating creak/click from the driveset for a couple of weeks; it comes and goes. I've looked around the many forums for advice on diagnosis & likely causes. I'm absolutely sure it's not the pedals (as I've put a fresh set on today). It's not the chain wheel (as I get the crea with the chain off) and I also get the creak out of the saddle.

This bit from Sheldon's website seems to describe the problem - I get a likely sounding creak/click by following these steps.

Bottom Bracket Cups/Retaining Rings Loose?
Because of the threading of normal bottom brackets, the cups are self-tightening to a point. This sometimes leads to careless installation, particularly on the right (fixed cup) side. If the right cup is slightly loose, it won't necessarily unscrew itself, but it won't really tighten itself up fully either. The symptom of this is an occasional creak or clunk usually as the left crank goes "over the top" when pedaling hard.

This is a surprisingly common, and frequently missed, casue of unwanted noises. Generally you should check the items above first, because they're easier to deal with. You can't reliably check the tightness of the bottom bracket mounting without removing the cranks, but sometimes you can diagnose it this way:
Turn the cranks so that the left crank is alongside the seat tube, wrap both hands around the crank and seat tube ans squeeze the crank hard toward the seat tube.

Then turn the cranks so that the right crank is alongside the seat tube and repeat this. Listen for a creak/click.

It's a sealed cartridge, square taper BB (with max 5k miles on it) in a Revoution Courier, if that's relevant. Does Sheldon's diagnosis apply to such BB? If so, is there any scope to adjust it, or its installation, to get rid of the creak?

There's no play in the BB, or none that I can feel. The creak is more pronounced with extra pressure on the pedals (obviously) and more so with extra pressure on the right pedal in particular. Would that mean I should focus on the right hand side of the BB if I do attempt an adjustment?

Or do I bite the bullet and replace?

Thanks in advance for any hints