If going the replacing parts route , then yes, try the LPFP. Having had the same codes with two different HPFP, makes it rather unlikely, but it cannot be ruled out.
This thread may shed some light. It suggests that at least some 3-series have a Low pressure fuel sensor, also that leaky injectors or certain vanos issues may be involved.
https://www.e90post.com/forums/showthread.php?t=943214
The problem here is the shotgun method, which usually leads to replacing things unnecessarily, as opposed to actual diagnosis and troubleshooting. Take it all with a grain of salt.