Plumbing – Removing pop up tub drain assembly

First, make sure that the clog is accessible via the overflow. Try this test... While the tub is draining slowly, pour water down the overflow through a funnel. If that drains fast, then the clog is in the horizontal arm and no clearing through the overflow will help you.

What works for me is to use a wet cloth to seal off the overflow (replace it first to make as small an opening as possible). With the tub 1/2 full of water and holding the wet cloth over the overflow vent, a plunger should then be able to clear the clog because it will force water down the drain (horizontal or vertical) rather than pushing water up the overflow pipe (or pulling air down it). Should that fail, use draino or physically pry off the grate for an auger.

The plunger should pull some amount of gunk back up into the tub while you're using it, even through the grate. If that doesn't happen and the drainage does not improve, then you may have a clogged vent. You need air behind water for it to drain quickly otherwise it's like water draining from an upside-down bottle. Cleaning the vent means going up on the roof and clearing the clog from there -- a hose at full blast will usually do this.

As for fully removing the overflow and parts... I don't know.

It may be time to call in a professional with a piping inspection camera system or rent such unit yourself and do an inspection of the drain line from the tub down into the sewer. This would clear up any concern that there may be a blockage or loose article that has entered the drain system.

The report that you had already removed a bunch of acorns from the roof vent line leads to concern that this vent is still clogged to the extent that free air movement below the tub trap is not being allowed and that the tub drain ends up with an air lock and thus cannot drain properly. It may be well to also scope out this line down from the roof with the piping inspection camera. (Do also make sure to install a screen on the vent pipe to prevent insertion of more acorns).

Since you already made attempts to clear the roof vent line is it somewhat possible that the vent was never installed correctly from the original construction and that this tub never drained properly. If that is the case then it may become necessary to install an additional vent pipe. The need for this of course could be eliminated if it was known of this particular bath tub did drain properly in the past. That could come from your own experience or consulting with previous owners.