Try adding a shim or 2 to the lpr. And use steel wool to polish the lpr piston shaft until shiny (don't take too much off or it will leak). Lightly lube the lpr piston and shaft. Run some oil down the sides of the tube where the lpr piston goes in. Spread it around the inside of the tube with your finger. Reinstall lpr piston. Put some oil again on the wall of the tube and spread. Cap it up, air it up, and let it rip.
Polishing the lpr piston helps with lpr recharge. Adding a couple shims ups your lpr pressure and helps make sure you lpr doesn't drop too much at a high rof.
If you still have shootdown, then I would clean and lube the minireg.