Most navis use the speed limit depending where you are to determine the arrival time. It doesn't want to liable for telling you to go 75 in a 55 zone.
The Navigation in the JX actually change the estimated time of remaining, may not be every seconds, but it is adjusting. When I was using it, it always shows I've 0 min left when I'm very near the destination.
The estimated time of arrival is computed based on the type of streets for the route. You can set the average speed that is used for calculating this ETA. Look in the settings and there are 4 types of streets (highways, residential, city etc) roads that all have independent speeds.
I like the navi quite a bit. I wish I could enter the exact place while the car is moving, but as far as routing etc it is great.
You temporarily override/bypass the restriction with the use of the remote (which can be paired with the homelink buttons on the mirror if you prefer)
Do what you need to do without the restrictions
And then turn the bypass off and back to normal
I would post a link to our site which show other cars like the FX35 working but not sure if that is permitted.
Look at the FX 2010+ Nav kit because that is the closest to the JX. On inspection of the wiring diagrams the FX and JX are almost identical. There are two extra pins occupied with the JX but we can easily allow for that with a JX kit.