Question IK with Timeline

I decided to give Timeline a shot with our new project, rather than using my custom solution. The custom solution was great for the previous project, but I feel it might be overkill for this.

I'm running into a problem with IK though. One of the characters needs to be carrying a tray, so I'm using OnAnimatorIK() to attach his hands to the tray. It works perfectly until I press play on the timeline. At that point, it still solves, but one of two things happens depending on whether I have Apply Transform Offsets or Apply Scene Offsets. If the first is checked, then the character's arms are perpetually behind him. If the second is checked, then it starts out correct, but it's like the IK goals stay in place while he moves forward.

I've seen other posts about using Rig Builder and such, but this is for mobile VR, so I feel like Rig Builder could be a bit too heavyweight for this.

Any insight on this behavior? What do I need to do to get the IK to solve the same as it does when the timeline isn't playing?