Alternatively, maybe try:
1. Scoop out the water in the bowl with an empty tin can or wax paper cup and finish up with a sponge.
2. Stick a small wad of Plumber's Putty in the jet hole at the bottom of the bowl.
3. Pour a whole bottle of acid based (phosphoric or hydrochloric) toilet bowl cleaner down the overflow spout. Toilet bowl cleaners are gelled so that they stick to smooth steep surfaces better, but that also means that they flow very much more slowly than ungelled acid.
4. As the acid collects in the bottom of the toilet bowl, set a funnel in the toilet tank's overflow spout. Collect the acid in the bowl with a plastic scoop of some sort and pour it back into the overflow spout.
5. Brush underside of bowl rim periodically to open up the rim holes with the brush bristles.

Keep scooping the acid out of the bowl and into the overflow spout for a day or two, and all of the rim holes should be wide open.

(I'd also consider plugging the rim holes that are clear and seeping acid with something very viscous, but which will dissolve in water, like honey, Nutella or even toothpaste.)

Toilet bowl cleaners are typically coloured so that you can easily see where the acid is and isn't. So, you should be able to see which rim holes are seeping acid out and which aren't.

Neither phosphoric acid nor hydrochloric acid will harm the glazed or unglazed porcelain of the toilet bowl; even if left on for long periods.