jermbob, you and I have VERY similar setups. We tow with a 2000 Ford F350 with the 7.3L PSD with a crew cab and the 8 ft. bed (very long wheelbase) and we're towing a 35' Jayco (Eagle) that weighs in around 8500-9000 lbs. depending on the length of our stay.
So as far as TV and TT go we're almost exact. However, I wonder what type of WD/sway hitch you're running. We have the Equalizer Brand hitch which has the WD and sway control together as part of the hitch. It's the 1400/14000 lb. hitch.
Our setup tows beautifully. That heavy duty truck should have no issues with your Jayco if it's right mechanically. Honestly our F350 tows our Eagle pretty well without any sway control/WD at all...and with a good setup like the Equalizer Brand it tows wonderfully.
I'd get that steering issue taken care of AND upgrade to either a Reece Dual Cam or the Equalizer Brand hitch. That sway controller you're running is too little for a TT that long IMHO..
JMHO