Shalom and thank you for your question!
The Mishna Brura writes (סי’ רפה ס”ק ז’) that from Minchah onwards on Shabbat, Shnaim-Mikrah for the coming week may be read, for the reason that you suggested, namely, since the congregation has already started reading next week’s Parasha, it is considered that one is holding with the congregation. It should be taken into consideration however, that the preferable course of action is to start Shnaim-Mikrah on Friday afternoon, and finish it before the Seudah on Shabbat during the day. (The Seudah before Seudah Shlishit.) If one did not manage to do this, then he may complete the reading by Minchah, if this didn’t happen, then one has until Tuesday evening. If one did not manage that, then it is possible to complete it until the coming Simchat Torah.
The custom among the Chabad Rebbes, was to have three times for reading Shnaim-Mikrah:
1. One or two sections on Thursday evening.
2. Friday afternoon, the whole Parasha in one continuation. The fifth Lubavitcher Rebbe, Rabbi Sholom Dovber, used to do this after immersing in the Mikveh, already wearing his Shabbat clothing.
3. Shabbat morning, the seventh section.
The reason for this custom was that in that manner they could satisfy the different opinions about it. How is that?
A. Starting before Friday morning suits the approach of the Holy Arizal.
B. Saying the whole Parasha (Sedrah) on Friday, satisfies the approach of the Shelah haKadosh.
C. Saying it in one continuous flow goes according to many accepted opinions.
D. Saying it on Shabbat in the morning suits the approach of Rashi and the Geonim.
The custom of the Tzemach-Tzedek, third Lubavitcher Rebbe, was to begin on Thursday evening, continue on Friday, and complete the reading on Shabbat in the morning.
