The OP needs to start from scratch and set up the hitch according to scale-derived numbers. No end of CAT Scales in the D-FW area. I used to use the one at the 35 junction near Denton, and another on 75 near Anna. Height measurements are okay for rough-in, but dial-in is the only way to get it right (and eliminate or confirm other problems).
Tire pressure on the trailer is to maximum sidewall number, always (cold).
TV tire pressure is -- within manufacturer door placard range -- according to scale weights also.
Real numbers generate a baseline that can be worked from over and over. Guesstimates are no ally. An old trailer like that -- with work having been done to it -- may have an improper tongue weight percentage . . and that can be fixed. But one first must know what it is.
No, the truck will not be as good as the T-reg, overall. But get the FA back to it's unitched number and see how the numbers are for the RA and TT axles and any further fine adjustments can make that item as good as it can be.
Then questions about "best" tow vehicle tires can be asked and answered with intelligence.
There are plenty of directions to go from this point onwards as well depending on the owners desire to leave no stone unturned.
Your rig ought to be able to outdo mine due to size, lengths and weights . . but I'd run circles around you, son. It isn't a competition, but it is about solidifying the basics of steering (accident avoidance) and hard braking (both vehicles in a straight line to one another to a full stop).
Break out (print out) the hitch manual, get a tool box ready, and get a friend to go to the truck stop with you for a few hours on a weekend early morning or late evening. Take your time, get the weights (re-weighs are $1), and do the work you're capable of (as shown in other threads).
2Airishuman's great thread (CAT Scale in title) is your guide. The WDH should show the FA at the unhitched value with WD adjusted properly and engaged, and the RA and TT axles should be something on the order of 60-40 to 75-25 percentage splits of the balance.
Once done, the possible range of adjustments is quite small for future loadings, tires or hitch.
1990 35' Silver Streak Sterling
; 9k GVWR.
2004 DODGE Cummins 305/555; 6-manual; 9k GVWR.
Hensley Arrow. 10-cpm solo, 18-cpm towing
Sold: Silver Streak Model 3411