I've searched but not getting the answers I specifically need.

I recently added a 3"/2" lift with Toytec 2.0 rear springs and 33" Cooper ST Maxx E rated tires and like everyone else my mileage and power has tapered off and I'm fine with the trade-off but now I've just purchased a 19' travel trailer at 4000 lbs. and I'm curious as what re-gear ratio would be good to go to?
I've had 4.56's on a 1/2 ton Ford I drove years ago with 35" tires and I hated the constant shifting so I'm not looking forward to that again. Would 4.11 or 4.27 be a good in-between?
This is not my DD but my weekend leisure vehicle that won't be used for towing every weekend but will be the only towing vehicle I'll be using for a while.
You guys with experience what are your thoughts?

I have 4.56 and its been great, no shifting issues, comfortable at highway speeds. It was regeared for 35's, I went with 32.5's.

There are really only two choices 4.56 and 4.88. 4.56 should work well for your needs. Don't expect better MPG...

Don't have much experience towing with the 4r. I can say that it is clearly not a great choice, but can probably get the job done. Consider an aux trans cooler and trying to stay in a low enough gear to keep the torque converter locked.

Re-gearing from stock 3.73's to 4.56's in a build 5th gen 4Runner with a lot of additional sprung and un-sprung weight should mean less shifting, not more.
If that's the only thing you were worried about, then I'd say go for it. Gotta tell you though, I'm perfectly fine with my stock gears and if what you said about your rig is correct, I'm carrying a lot more extra weight than you are. No trailer though.

First off that Ford was irrelevant. Final drive is a combination of transmission and difs. Ford Transmissions are usually much different from Toyotas. That's before we even discuss the difference between a v8 and a v6.

Toyotas transmission and dif choice was unnecessarily tall in order to get good MPG ratings. For real world driving the 4.56 with 33s is amazing. One of my favorite mods.Makes the final ratios lower and closer which reduces shifting and improved my in town and mtn road mpgs. flat highway was worse but if you are towing a 4k trailer with the 3.73 good luck ever seeing 5th gear in your current config outside of going downhill.

This. Comparing a Toyota and a Ford is like comparing apples and crap.

I towed a 3500# pop up trailer without searching for gears. And with larger tires and weight, it was fine with 4.56's. I think 4.88 would be too tall.

I recently went on a 2500 mile trip to the mountains with my 4.56 gearing and 34" MTRs. Overall, I was impressed. Never lacked power (did not notice the altitude drop like I did with stock gearing) and actually got close to 17mpg going up there... avg around 72mph (mostly tried to stay 75mph but went 80 here and there). Granted, I think I had a tail wind, because on the way back it dropped down to almost 14 at times with a steady head wind, plus I went a little faster.

I did shift it manually... mostly on mtn passes, because the trans was starting to get up there (230) letting it do its own thing. I also like engine braking, and the control of shifting it myself.

But, I can't imagine towing an additional 4k with it on anything but flat ground. I'm sure it will do it, but expect a bit of a struggle. Depending on the profile of your trailer.. you may also be adding some significant wind resistance. I pull my trail rig all the time and it is like a sail up there on an open trailer... Wind resistance is a major factor to confider....

suggestions on what gear ratio I should use with 33s and a 3"/2" lift. I very seldomly tow anything. was wondering what stock was and this thread came up

https://tiresize.com/gear-ratio-calculator/

this might help

turning a little more RPM is better than turning a little less.

If you don't change gears at least use 4th in sport mode so it won't slip in and out of 5th and smoke the converter. I wish we got 4.10's stock!