Two year visa (L) with entry requirements (e.g. 30 days maximum stay before leaving and returning)? Unless I'm mistaken, L visas cannot be converted into permits. You'd need to apply for an X (xuexi/study) or Z (gongzuo work) to be eligible for a residence permit. Other visa categories including M (maoyi/business) and F (fangwen/special visit) also limit how long you can stay at a time, same as an L visa.

When I was there, they also had two subcategories of X visa - short study (fewer than 180 days) and long study (180+). Only the latter was converted into a residence permit.

According to the China Daily website, you can apply for visa changes after arrival, subject to some general conditions, and specific conditions for specific visa types. https://govt.chinadaily.com.cn/s/202204/01/WS62d8bbd1498ea2749279ef2b/guide-on-visa-extension-change-and-reissuance-for-foreigners.html

Commonly, people will hop over to Hong Kong, Taiwan, Mongolia or South Korea depending on where they are in China and what's convenient/cheap and apply for a new visa at a China Visa Centre in that country.

Asking at an Entry Exit Bureau can't hurt if you wanna fully explore what your options are. It'll be a good part of your day gone, but could be informative. Of course this is also kinda putting the cart before the horse. If all you want is a bank account and it turns out you don't need the permit for that, then it's moot.

Edit: also please do report back because I'm super envious and wish you every success