Questions about visas and mainland trips

My question is similar to one down below about Xiamen. I will be in Taiwan soon studying Chinese, and so will have to go out of the country periodically for the stamp on my visitor’s visa. I’ve been told this is easy to do - you just spend a few days in Hong Kong - but it’s expensive for me, as I will be on a fixed income and have to get a plane ticket for my husband and little boy as well. For the year we plan to stay, two or three trips to Hong Kong sounds pretty expensive, tickets being around $500 a pop. I’ve been told that there is a ferry to Xiamen from Taipei, and was hoping to get my ‘yes I left the country’ stamp there instead of Hong Kong. Is this possible? Or is Hong Kong the only place on the mainland that can give you the right stamp?

Or I should say, is Hong Kong the only place where your paperwork can be handled properly? Is it legally the only Mainland place you can go?

Or I should say, is Hong Kong the only place where your paperwork can be handled properly? Is it legally the only Mainland place you can go?