The artistic license talks about modified and standard releases of a package, but nothing is said about chunks of code. Of course nobody here is a lawyer, but can you find something reasonable in the license allowing to take chunks of code from an AL project and putting the code verbatim into a BSD licensed project ?
I think there are probably two things which would allow you to do this.
The first is that Wikipedia classifies AL as non-copyleft, which leads me to believe that you can integrate the source into a BSD license, as long as you follow the other provisions of the license.
It looks like what you want to do falls under 4b in the AL:
(4) You may Distribute your Modified Version as Source (either gratis or for a Distributor Fee, and with or without a Compiled form of the Modified Version) provided that you clearly document how it differs from the Standard Version, including, but not limited to, documenting any non-standard features, executables, or modules, and provided that you do at least ONE of the following:
…
(b) ensure that installation of your Modified Version does not prevent the user installing or running the Standard Version. In addition, the Modified Version must bear a name that is different from the name of the Standard Version.
So I think as long as you don't call it by its original name, and it doesn't interfere with the functioning of the AL-licensed package, you should be able to lift the code and place it in a BSD project, as AL is not copyleft. I think, however, that the code would still remain under the AL, so you would now have a part BSD, part AL project. Just a best-effort guess though.