I have the same problem. There's still a tick after replacing the timing parts.
I actually had 24 new lash adjusters and roller followers when I had the front cover off. I even had the freedom racing valve compression tool. But I didn't replace them.
I was running out of time. And for the life of me I couldn't get the freedom racing tool in towards the firewall. It's pretty tall. Maybe it's for a mustang.
I did find that to replace the roller followers and lash adjusters on a 5.4, you have to remove the camshafts. I tried to get to the lash adjusters without removing the camshafts, believe me. I could get the roller follower out, but the cam lobe blocks the lash adjuster.
In the ford shop manual they pull the roller followers, disconnect the phaser, and pull the camshaft. Then the old lash adjusters are replaced. Then the cam goes back on and then roller followers and finally the phaser.
If I could have figured out the valve compression tool I had I would have done it. But I didn't so that's a project for next summer.
In the meantime I'm enjoying the startups without chain rattle.
2004 F-150 XLT
New Body Style
5.4 3v 4WD Auto with Electronic Shift on the Fly