I've decided to give "Sport" mode a little test. First thing is that it seems to alleviate the "hunting" syndrome better, but I need to drive a few more miles to be sure.

 

You have various levels of the Lurch.
Have you read this?

Jaguar S-Type Ownership Experience - The ZF LURCH Fault

He is kinda over the top but has good information about the different kinds of the Lurch.

Have you had the TCM flashed by Jaguar to the latest software version?
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I did find something that drastically improved my 1st gear lurch. I cleaned the MAF sensor and it did get a bit better, but I noticed at this point that the previous owner had installed a K&N. It had fouled the MAF on my GTO regularly as well and required constant cleaning. I bought a standard paper filter and within a day of driving now the lurch is basically gone. I'm not sure what was the biggest contributing factor, but it may be worth cleaning the MAF and getting a new air filter if you haven't done this recently. I now can use standard mode comfortably again.

 

Some of you guys know that me and my first gear do not get along most days, it doesn't give me major issues.. But it doesn't shift where I want it too, and other ZF boxes I have experience with are not as temperamental...

Anywho, I haven't been driving the xjr but for maybe once a week. It occurred to me to do a small experiment, if my first gear issue comes from what I assume to be an early shifting issue why not try and see if under normal circumstance driving the car in sport mode will make a significant difference.

Usually from the stop, it shift in between 8-1k rpm, unless I am fiesty and get the rev range up to the low teens, then I would not recieve any flare.

Obviously that isn't optimum because you don't always want to be so aggressive from the stop for a number of reasons.

The last three times I have driven the car, I have only used sport mode. It is completely different, when crawling from a stop i recieved no flare what so ever.

Like others said, the higher gears do hold longer, from my limited driving only using sport (50~mi) they seem to hold for an average of 15-20 seconds longer than if sport wasn't engaged.

Sixth gear does engage in sport mode, I tested that out with the J gate. Shift back and forth between 5 and 6 just as it would in non sport..

Interestingly enough, the higher Rev level in gear change under "normal" driving conditions don't really seem to be far off from the changes in the non sport mode, seems to be around 500-600rpm. Obviously under load the shifts are much more open, and the downshift under WOT gets an extra gear drop.

I won't be driving that car if it's not in sport mode anymore. The 2mpg it might siphon is worth the smoother ride.

Sorry to bump the older thread, but it came up in Google when I searched just now to see if others experienced this.

 

It will go up 6th in sport mode if you engage the cruise control (strictly speaking that's a third mode ... 'cruise-mode')