New bath- slow tub drain

I have a new 5' jet tub with all new plumbing from tub to basement that seems to drain slow. I get about an inch of water about a foot around the drain when showering, and full bath takes a long time to drain.

The tub drains into a 2" trap into a 2" line that runs 4' under the tub and drops 12" @45deg and turns 90deg (long sweep), runs 5' and picks up a 1 1/2 vanity (twye), runs 3' and into a 3" line eventually to the stack. All drains have at least 1/4" pitch. I have removed the trap and drain which are clear.

Here are my thoughts:
1. The trap is too big? Should the trap be 1 1/2 so the 2" drain line does not fill completely while draining?

2. Venting? There is no gurgling when the tub drains. Does this mean that vent is ok? Since the drain lines run under the tub, I used a 2x2x1 1/2 san tee at the outlet of the trap and ran the vent up the front wall of the tub. I realize that this is not ideal, but it is what I had to work with. I also put a cleanout in the tub compartment where it makes the 90deg turn. I have since put an aav in the cleanout to see if it would help.

I have another tub in the house with extremely poor venting (sounds like a belching cow) and it still seems to drain much faster than the new one.

Any ideas will be welcome. Thanks.

a couple things to consider: the tub drain opening may be smaller than what you are used to-i have seen some small openings in certain drain fittings made by certain manufacturers. something else to consider-with the new tub came new walls, did you put in the new walls or have someone else do it? maybe something got down the drain during wall construction? you could remove the trap below, stopper up the tub fill it up a bit and then release the water and see how it drains, in a finished basement or a room without floor drain have it drain into a large empty garbage can to be dumped out afterwards, if it still drains slow with no trap you can assume the problem is not with piping but with tub drain fitting itself or obstruction in tub drain fitting

I cleaned out the tub drain setup and the trap after I finished construction to make sure nothing got lodged in there. It did seem like the opening in the drain where it meets the extension pie was very small, definitely not 1 1/2". This is a brass Kohler product, my other tub has a brass Gerber product. I will compare the clearances tomorrow. Everything is still accessible, so changing the drain would not be a problem.

A drain that is really running fast will suck air in while draining. If it belches air bubbles out, it's got problems, but sucking air means it is actually running well.

Where is the trap in relation to the drain of the tub? I don't think a 2" trap would make any difference verses a 1.5" one in this case.

If it is open enough, take a picture and post it...it should give the pros a better idea what's there and how it is installed.

I compared the drains on the 2 tubs and found that the Kohler extends about 2" down from the bottom of the tub while the Gerber extends almost 3". This could be just enough to slow things down. The Kohler just looks way more restrictive in how it's designed. Perhaps I'll swap drains to troubleshoot. I'll try to shoot some photos.

fixed

I switched out the Kohler brass waste and overflow with the Gerber 17ga unit. I put the two side by each and easily noticed that the shoe on the Gerber is about 50% larger than the Kohler. Standing water no more!