So can the 89fzr400 wiring handle twin 55W/60W halogen globes instead of the 35w/35w standard globes?

Fit relays.
The wiring will warm up not by much but it will harden the insulation over time

I guess the other concern is if the charging system will keep up. With the brakes and blinkers on I find the headlights (35W) dim in slightly while idling at the stoplights.

You don't want to put such power through the handlebar switches, much more there are two of them!

That's right, you should use relays. And preferably use new wiring, separate for the headlights (They became the highest power consuming parts of the entire bike) and you also eliminate most of that dimming and voltage drop issues.

I once torn apart an FZR1000 loom and shocked how they just tap wires along single power lines...bad piece of engineering, but hey, they work fine...until you decide to get more powerful horns and lights on. Maybe even a sound system?