It sounds like a perfectly normal reaction.
The 'problem' (not really a problem as such, just a learning curve) with doing a bit of both types of feeding it that they learn to suck purees off off the spoon without chewing them, and then try to do the same with solid food, hence the gag.
But the gag reflex is very effective and completely normal, and is she is sitting upright and left to her own devices, she'll be fine.
As said before, it's best not to help her as she is not in full control of what she is doing then. If she's finding food slippy, give her bigger chunks with some skin left on- I used to just slice a ripe pear lengthways and give it to Ds2 at this stage - much easier than little strips.
Other ideas for non slippy but easy to eat foods are roast potatoes, or roast butternut squash. In fact most roast veg is easier to handle than fruit. Slices of melon with the skin on is also good - they're known as melon smiles in our house!
She sounds like she's having a lovely time. Give her well cooked food in sizeable chunks, make sure she's sitting upright, not reclined in a bouncy chair or carseat, and be brave and let her get on with it 
BLW is much a brilliant way to introduce babies to food. They have such fun with it, nad progress in their own time. Keep the faith!