I've been down this road before. Newer model short bed quad cab F150, a 33' trailer weighing about 7k lbs loaded, and that same EZ lift setup. What follows is probably not what you want to hear:
-There is no way your truck has a 3k payload. Even the HD150's that get around 2500 are ALL on 6.5' bed platforms. You are probably in the 1600-1900 range.
-Your rear axle is likely overloaded. This can be compensated with more WD but only to a point, you don't want to push the front down more than unloaded.
-That hitch is terrible. I've towed three campers now total and have used the EZ, an Equalizer, and now a Hensley. I would absolutely never tow another mile with the EZ. Mine was so bad I bought a used Equalizer on Craigslist while five hours from home and installed it at the RV park just to get home. Even if you get the WD done right, the sway control is a different function of the hitch and I think the EZ is a terrible design.
Ultimately I ended up with an F250 and a Hensley hitch, but I don't think either of those are necessary, they were just worth it for the peace of mind for me.
AT A MINIMUM: Buy an Equalizer 10k/1k or simar style known brand WDH. Read the manual and watch YouTube until you can explain what each adjustment does to someone who has never camped. Hit a CAT scale to dial it in. Lots of those hitches can be found used under $500 and trust me, it's a small price to pay. I would be buying E rated tires too, but you gotta make your own choices.
You are right at the brink of what *I* think a short bed F150 can do. That would not be a tow the RV out west setup for me, but it can probably be adjusted to be safe and useful on easier stretches of road or close trips. You should be cognizant of overloading the truck and trailer and pay attention to your axle ratings along with all the others. I ended up 300lbs over my rear axle rating with a properly adjusted Hensley hitch, and that was leaving all firewood, spare fuel, and bottled water at home. IE, packing super light.
You can probably get there, but I don't think you ever will with that EZ setup.
