As you've probably figured out, there is a segment of the motorcycling community that thinks that you're not a real man if you don't ride the bike everywhere. You can buy stickers that say "If you see this bike on a trailer, its been stolen. Call xxx-xxx-xxxx." The guys who feel this way generally look down their noses at folks who use trailers.
My view is that they are often masochistic. Running a bike up the eastern seaboard in July or August from Tennessee to Maine is not my idea of fun. The traffic on the slab is horrible most of the time, temps are often in the 90's or worse, afternoon rains can rival those in the days of Noah, and no matter how big the bike is, you'll have a hard time keeping clean clothes handy unless you're will to do laundry every couple of days. I'd rather haul the bike into southern New England, or the Adirondacks, and then enjoy the riding without the slabstress. And when traveling with wife and dog to a motorcycle friendly destination, the a/c, sound system, and comforts of lots of space, room for snacks, virtually unlimited luggage, etc. make the truck and trailer package a very high comfort indeed.
I run I-40 on bikes a few hundred miles at a time all through the year on in-state errands. I just don't want to do it day after day when the trip is supposed to be for fun.
So .... getting to your question.....
Yes, it is not a bad idea to tie the front wheel into the chock. You can use a velcro strip, or a small clamping tie down.
The key is to remember that you did it. If you try to duck walk the bike back out of the chock, and you've still got it in gear, or you've still got the front wheel tied in, you'll end up frustrated. Sometimes it helps to make a check list to be sure you've covered all the bases.
FWIW, on the FJR I found the Cycle Cynch handlebar tie system to be really nice..... easy on the bike, yet secure.
You can also tie the back wheel in. In my old trailer I used to wrap the rear wheel close to the floor and then tie to the D rings on the left and right. This method allowed me to secure the trailer without removing the saddle bags.
Good luck on your trip and have fun.