Is there a prophetic date for the anti-typical Feast of Tabernacles, just as there is for the antitypical Day of Atonement beginning in 1844?

Answer: Yes and no. The central spring festival is situated by date, and the central fall festival is situated by a specific date in the fulfilment of prophecy. The fulfilments of the other feasts cluster around those two prophesied dates.

The spring feasts of unleavened bread, Passover, and the feast of weeks are dated in Daniel 9:24-27. The dates given in Daniel focus on the earthly ministry of Christ, his baptism in 27 A.D., his crucifixion in 31 A.D., and the Gospel extended to the Gentiles in 34 A.D. The dates do not correspond to the spring feasts specifically and individually, but center on the events of Christ's earthly ministry, particularly on the middle event, Christ's Passover sacrifice of himself.

The fall feasts are dated in Daniel 8:14. The feast of trumpets, Atonement, and tabernacles have their anti-typical fulfilment in the global great second advent movement, the entrance of Christ into the Most Holy Place of the heavenly sanctuary in 1844, and the post-advent events. Again, the specific date focuses on the middle event in 1844. When the anti-typical Day of Atonement, which began in 1844, is finished, then we can look for the fulfilment of the feast of tabernacles.

We should always bear in mind that only the Father Himself knows the day and hour of the second coming. We cannot predict a date for that, and we should not try to do so, as it is a distraction from our God-given duties.