If you're finding it distressing, then BLS may not be for you; as a key element of BLS is trust. Trusting that your baby can choose what she wants to eat, trust that she can work it out for herself etc... If you're worried and anxious, this may not be enjoyable for you -so maybe go with the mashed foods instead.

BLS is centred around the ideas that even though we hold off solids until six months, we're still introducing purees and mash - something suitable for a three-four month old. Your baby may not be yet ready to handle going straight to BLS - but FWIW my DS gagged more often on mushy food than on the food he had control of, and I have heard many other BLS mums say the same!
It will take time for her to get the hang of it. If you are following the food is fun until i am one mantra, then gagging is a 'good' thing - it is her learning how to control her food. DS would gag, spit it out and try something new. Taste and texture, not eating. If you do go down the route of a more pureed consistency - try mashed instead of pureed, as it is still giving her some texture to work with.

Sorry for ramble, very late and tired/!