I have tried both CLR and Limeaway on various surfaces and IMO those products are totally useless.
Vinegar totally outperforms both of those products but for heavy deposits the vinegar has to remain in contact for 24 hours.
On faucets, I wrap them with vinegar soaked paper towels and respray them every chance I get. After the initial cleaning a quick spray every other week or so (w/o the paper towels) keeps the problem from coming back and my 10 year old faucet looks like new.
So barring a better suggestion, I would pump down your bowl water and spray with vinegar, and put some paper towels or cotton towels around the ring to keep the vinegar in contact (respray as necessary). After 12-24 hrs or as long as you can bear, some light scrubbing should easily lift the deposits. If you have barkeepers cleaner you might use that to get a little additional scrubbing action.
Anotehr trick I have heard is to pump down the water and dump a bottle of cola soda into the bowl and scrub it.
I wouldn't use mechanical methods as I have seen the mineral deposits lift the chrome plating from faucets.
I still can't believe how good my faucets look since for 20 years I lived with terrible looking faucets.