Are you wanting to go straight to the stomach because you think she really can't swallow it? or because you feel the method will be easier?
I'm not a vet! but in nursing, when it comes to humans, you always try and promote people to do as much as they can on their own. Which is why we hand feed people, and not just stick tubes in them.
They do much better when they can at least do a tiny part of their task, "use it or loose it" theory.
I would take this approach with your dragon, thickened liquids are the easiest to swallow, they don't go down too fast, so choking hazard is lessened.
If you do decide to try and feed into the stomach you can probably get past the epiglottis easily, (as long as the epiglottis is functioning normal. It covers the trachea, and in relaxed state leave esophagus open) But there is also the sphincter that opens and closes from the esophagus to the stomach, if you hurt that sphincter stomach acid can damage the lining in the esophagus.
All this info is based on human anatomy, but I do believe the basics of the digestive tract are pretty similar.
Maybe talk to your vet and they could teach you how to do it properly before you attempt on your own?
Good luck, I hope your beardie gets better!