From what I understand the Torah only forbids a man from relations with his wife while she is on her period, until she goes to the Mikvah. The Rabbis decided to add the additional days as a stringency to make sure she is pure and the period is over.
Are there any modern opinions or movements that allows the woman to go to the Mikvah at the end of her period and not wait a whole week?
The law in Leviticus says:
For normal periods , she's impure 7 days and can then go to mikvah. The period could end of Day 5 and she'd still be impure for all 7.
For flows "many days more than normal", she waits for the flow to end and then needs 7 clean days.
As you indicated, the practice that came into force in later Talmudic times is to avoid questions of "normal" vs. "more than normal", and thus to wait 7 clean days for everything.
So the whole question is whether "7 clean" can be omitted if we're certain this is a "normal" period (that gets tricky), and instead to count seven impure days from the start of the period (assuming it ends before 7).
From what I recall there was some theoretical discussion in the Conservative movement of going back to the biblical practice; practically most people either keep today's standard practice (wait 7 clean) or don't routinely keep mikvah laws.
A "kiruv" rabbi in Orthodox outreach asked his mentors if he could tell a couple interested in increasing their observance to omit the 7-clean practice; they said no.
You are dealing with a very central issue. What is simple is always a bit wrong; but it may be good as an introduction, and you are going to understand why a secure common way has been setup by our teachers for all without exceptions and without possible recourse.
A first notion that we want clarify is the notion of close of the Talmud, see Rambam in the introduction to his Mishne Tora:
.. הוֹאִיל וְכָל אוֹתָם הַדְּבָרִים שֶׁבַּגְּמָרָא הִסְכִּימוּ עֲלֵיהֶם כָּל יִשְׂרָאֵל...
The entire people of Israel accepted everything is decided in Talmud.
An important point is a testimony of the Talmud (Nidda, 66A)
אמר ר' זירא בנות ישראל החמירו על עצמן שאפילו רואות טפת דם כחרדל יושבות עליה שבעה נקייםand Brachot 31A
R`Zera stated: The daughters of Israel have imposed upon themselves the restriction that even if they observe a drop of blood of the size of a mustard seed they wait on account of it seven clean days.(Soncino's translation)
ת''ר אין עומדין להתפלל לא מתוך דין ולא מתוך דבר הלכה אלא מתוך הלכה פסוקה והיכי דמי הלכה פסוקה אמר אביי כי הא דר' זירא דאמר ר' זירא בנות ישראל החמירו על עצמן שאפילו רואות טיפת דם כחרדל יושבת עליה שבעה נקיים
Our Rabbis taught: A man should not stand up to say Tefillah either immediately after trying a case or immediately after a [discussion on a point of] halachah; but he may do so after a halachic decision which admits of no discussion. What is an example of a halachic decision which admits of no discussion? - Abaye said: Such a one as the following of R`Zera; for R`Zera said: The daughters of Israel have undertaken to be so strict with themselves that if they see a drop of blood no bigger than a mustard seed they wait seven [clean] days after it.
After this important introduction, We can examine in Parashat Metsora two kind of "uteral bleeding": the first is called Nidda and the second Zava. The first refers roughly to healthy menstruation, the second to an intermenstrual bleeding. Normal (healthy) bleeding ends naturally within 7 days. An illness ends when the woman heals. There is an alternation between Nidda and Ziva (intermenstrual bleeding) periods. We may lose count. A range of interrelated stringency will make us sure that there is no sexual intercourse in a banned period. In nidda the uncleanness is 7 days, after this, in the first evening after 7 days, immersion in mikve allows marital relations. In Zava gedola, a count of 7 days without bleeding is required, after this, in the middle of day 7, before the evening, immersion may permit marital relation. We have the custom to wait the evening because the original tevilat nidda is in evening (op cit).
If necessary we getting more technically into the substance of those laws, through Rashi in Megila 28B and rabeynu Yona in Rif Brachot 21B.
I would guess The Tzedokim and the Karaites but only by a unusual blood Discharge that is not for 3 days, not for her period it is 7 days
Biblically.
vayikra 15.19
nidda can be pure after 7 days even if blood everyday.
(Zava is when blood comes after the 7th day (this is not considered her period anymore) until the 19th day). Vayikra 15.25 many days means 3 days
a Zava ketana can be pure the next day one day (since she knows she is not a Zava gedola)
a Zava gedola (when blood comes 3 days in a row not during the time of her period) can only be pure after 7 clean (no discharge) days
But the rabbis and then the woman except stringencies opon themselves (which are honorable to G-d).
Nida 66a
R. Joseph citing Rab Judah who had it from Rab stated: Rabbi ordained at Sadoth, If a woman observed a discharge on one day she must wait six days in addition to it (she might be a nidda) If she observed discharges on two days she must wait six days in addition to it (she might be a nidda) If she observed a discharge on three days she must wait seven clean days (she might be a Zava gedola). R. Zera stated: The daughters of Israel have imposed upon themselves the restriction that even if they observe a drop of blood of the size of a mustard seed they wait on account of it seven clean days. (They might be a Zava gedola)
Today, some decisors still take this route. Others recommend in vitro fertilization using the husband's sperm as a better choice.
But this isn't a general ruling. It relies on the mitzvah of procreation trumping the later laws of niddah. So it's not an answer to the question.
– Micha Berger Apr 05 '16 at 19:25