All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
What has been reported in the Hadeeth of the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, is that the reward for offering a prayer in Al-Masjid Al-Haram or within the limits of the sacred precincts of Mecca is multiplied. This means that the reward for a single prayer equals the reward of one hundred thousand prayers offered elsewhere. The Prophet, sallallaahu ‘alayhi wa sallam, said: "One prayer in this Masjid of mine is better than a thousand prayers in any other Masjid except in Al-Masjid of Al-Ka‘bah (in Mecca)." [Al-Bukhari, Muslim, Abu Daawood, An-Nasaa’i, At-Tirmithi and Ibn Maajah]
The version narrated by Imaam Ahmad adds the following: "... and a prayer in Al-Masjid Al-Haram is better than one hundred thousand prayers." [Ahmad; Shu‘ayb Al-Arnaa’oot: authentic]
As for the rewards for reciting the Noble Quran in Al-Masjid Al-Haram and whether or not they are multiplied with such a number, we have not come across any evidence that supports that view. However, the rewards for righteous deeds, in general, are multiplied in the sacred places. One of these righteous deeds is the recitation of the Noble Quran. Nevertheless, the mentioned multiplication pertains to the reward only and does not mean that the person has performed the action itself for such a multiplied number. Hence, if a person has to make up for missed prayers and then performs only one prayer in Al-Masjid Al-Haram, this does not suffice him nor would it be counted as a valid fulfillment of the obligation of making up for the missed prayers. Rather, it would be counted as only one prayer whose reward is equal to that of one thousand prayers elsewhere, as we have outlined earlier.
Hence, it is incumbent on you to recite Surah Al-Kahf one thousand times as you vowed. Reciting it once in Al-Masjid Al-Haram or elsewhere will not be sufficient for you.
Allaah Knows best.