Tub drains very slow
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.