Huh, excellent idea. I got nothing to lose so...

Yes, cleaning the nib may help, as well as cleaning/flushing the feed of the pen itself. If you have tried a few inks and types of paper, I would imagine it's indeed a faulty nib, but I would thoroughly clean it first. Just to be sure there is no residue left from the manufacturing process.

You can use lukewarm, water to do that. If that is not enough you may add a tiny drop of dish soap (like a tiny, tiny amount of it, noticeably less than a drop) and rince it again. After that, you should let it dry thoroughly. I often let mines dry for a few days but unlike you I'm in no hurry. The pen will dry faster if you remove most of the water, obviously, but don't try to heat it to accelerate the drying process, as you risk damaging it.

I've cleaned it twice using dishwasher soap and water, the usual treatment. With full disassembly. But if there’s a more thorough method I'll be glad to try.