I finally have some time to address some of the points mentioned in the OP that I thought were pretty interesting when I first came across this thread.
I've been reflecting a lot about my own spiritual life lately, and coupled with all of the heavy reading I've been doing for class, this question came to mind:
Is there such a thing as Tantric Vaishnavism?
Not tantric as in a left hand path (vamachra), but also not completely falling within Vaishnava orthodoxy?
What exactly is Vaishnava orthodoxy? If you are referring to Ramanuja's original siddhanta, then I'd say very few SV actually follow it thoroughly and without any outside influence from Advaitic/Smarta sects.
Differences in beliefs is not prohibited in Vaishnavism/Vedanta. I don't know how this modern perception of Vaishnavas as some fundamentalist zealots who don't think outside of their sect managed to overshadow the centuries of Vaishnava contribution to the advancement and evolution of Hindu and Vedantic philosophy and cultural traditions.
Krishna and Ramanuja both tell their followers to deeply analyze their works, and then decide what they wish to do. As long as you fit the basic criteria for a Vaishnava, you are one despite your minor disagreement with the norm. This is why ancient Advaitins, Vishistadvaitins, and Tattvavadis could all be termed as Vaishnavas despite their numerous and major disagreements.
- Don't have such a restrictive view on sex (as in I don't see non-procreative sex within the context of long term commitment as "illicit")
Most modern Vaishnavas would probably agree with you. I personally don't see a difference between marriage and a long-term relationship.
- View scriptures more philosophically, mystically, and esoterically; instead of always straight up literal.
Again, most modern Vaishnavas would agree with you. The philosophical meaning of texts is more important than the literal meaning because it is something you can actually apply in your daily life or gain some insight from. For example,
The Handmaid's Tale appears to be a great book on a theocratic state that restricts women's right, but if you read one or two levels deeper, the book's commentary on sexuality, fertility, identity crises, and politics are simply brilliant.
- Place little emphasis on most Puranas, to the point where most of them are not very important in my practice. Or I just flat out reject some of them (like the Garuda Purana). I also reject the Manu Smriti.
While Puranas may be on the bottom of the list in terms of scriptural importance, they certainly are worth taking a look at if you haven't already. Bhagavata and Vishnu Purana have been praised for their simple commentary on bhakti that is both profound and comprehensible.
- I place a lot more emphasis on Shakti (Sri Lakshmi) than an average Vaishnava. More so than what is considered normative for Vadakalai or even Gaudiyas.
I can't imagine this being a negative.
- Unless one is a priest or acharya, then I firmly believe that ones intentions or faith in doing rituals is technically more important than "doing them right". As in I don't think God will strike the average householder down if they mispronounce a few Sanskrit words or don't use the exact kind of materials as prescribed in scriptures.
Really good point, agreed.
I personally think that you are looking too critically at your role as a Vaishnava, and I don't think any of your above beliefs would deny you from proclaiming yourself a Shri Vaishnava.