Hi M., I feel your pain. I'm working through the same issue with my near-17-month-old son. He has been on the slow side in regards to adapting to table food and has a very sensitive gag reflex, but we're getting there! So, don't fret: your child won't be on baby food forever.
Key things are to be patient (with him and with yourself), ignore people's advice to withhold the baby food and offer table food only (I, personally, think it's wrong and in most instances fruitless to push kids' development) and take it slow, preparing for some backslides along the way.
Here's what is working for us: When my son was just about 13 months old, we had some success feeding him super-whipped (i.e. no lumps) mashed potatoes off of our fork. We didn't have him try to self-feed; instead we wanted him to get used to the texture and enjoy table food before asking him to feed it to himself. This strategy is working well for us, and we've been at it for four months.
With time, we have graduated to finger foods such as avocado, bits of brown bread or inside of a croissant, teething biscuits, orange that has no membrane, boiled carrots and peas, and peeled and quartered grapes. We still feed him stage 3 food and/or lentil soup and other from-the-spoon/fork foods, so we haven't yet fully transitioned to table food and self-feeding. But we try to have a good mix of both with every meal, keeping in mind that some meals end up being baby food-only; my opinion is that it's OK as long as my son is getting nourishment.
Try to take cues from your child and be prepared to take it slow. He'll let you know when he's ready for the types of foods you are offering.
Good luck!!