I have now (mostly) successfully moved from Joomla3.7/jFusion2/phpBB3.0.x to Joomla3.7/p8pbb/phpBB3.2. The move itself did not give raise to any particular issues, although I have a couple of problems related to wrapped mode (which I have raised in support tickets).
Here are the steps I took for a successful move:
1) Disable all jFusion MODS for phpbb, using the jFusion configuration panel for the pbpBB plugin (redirect MOD, dual login MOD, frontend moderator panel MOD)
2) Disable the jFusion plugin itself (master button on the main page of the jFusion component)
3) Re-enable the Joomla user and login plugins
4) Uninstall the jFusion package using the Joomla extension manager.
5) Log in + check that Joomla and phpBB function fine separately.
6) Moved Joomla to root folder (This may not apply to others. But I previously had both phpBB and Joomla in subfolders).
7) Upgrade phpBB to latest version (optional, but since I was stuck all the way back on 3.0.x I decided to do some major house cleaning and move to 3.2)
8 ) Install the p8pBB package in Joomla and configure according to instructions in the PDF provided (must be read
very closely).
9) Install the jprosilver (wrapped) template for phpBB. Set it as the (only) default.
10) Test dual login etc works when phpBB and Joomla are "standalone" integrated (i.e. not wrapped).
11) Set p8pbb integration to "wrapped", and add the p8pbb menu item pointing to the forum.
12) Fix whatever CSS bugs remain, install extensions, enjoy your fresh install, etc
