@ Author,
Thank you for asking concluding relevant que. of your presented brief.
In case one of the parties is a foreign national, no objection certificate / marital Status certificate from the concerned Embassy should be sought which is the only thing to pay more attention in presented brief of yours is my observation;
Also refer to https://www.state.gov/documents/organization/86802.pdf especially Part 7 FAM 1453.2 as well as Part 7 FAM 1455.1 and in my opinion State Dept. has not repealed and or omitted till date this .PDF file so it is a valid source!
Reasoning:
For both of your peace of mind also refer to Law in India under Special Marriage Act, 1954 by referring to Bare Acts Forum of LCI.
Here are Laws of the land on subject matters basis which my reply stands on its own feet;
Issue - Section 1 & 4 - Marriage between foreign national and Indian - Whether the marriage can be solemnized of an Indian Citizen with a foreign national in India under the provisions of the Special Marriage Act, 1954.
Held A foreigner can get married in India with a girl of Indian Nationality under the provision of the Special Marriage Act 1954. Any two persons in India, where one of them or both of them are foreigners or both of them are Indians can enter into a form of marriage under the Act.
Authority Referred - Vatsala & others vs. Sub-Registrar and Marriage Officer and others Kar L.J. 1981 (1) 294
Held Section 4(a) states that marriage between any two persons may be solemnized under this Act if neither party has a spouse living. All that it says is that if either party has a spouse living at the time of marriage, the marriage can not be solemnized under the Act.
Authority Referred - Paramenshwari Bai V. Muthojirao Scindia AIR 1981 Kant 40
Also read SC (authority) post at https://www.lawyersclubindia.com/forum/Hon-ble-SC-on-Registration-of-marriage-23614.asp
Lastly if you are still not convinced by my replies then feeling that you are from my lovely hometown read down official State website https://mumbai.usconsulate.gov/marriage.html yourself and once both of you are happily marrried off before flying on your honeymoon comeback to this post and thank LCI to have given both of you a platform to be now happily married off :-))))))))) just kidding....................on this note I close this post from my side and maybe other subject experts may throw their ld. wisdom if required by both of you.............
All the best.