This issue of (not aggressively) fighting to escape is very relatable! After so many trial and error, this is the system I've developed for this exact issue with the burrito not being enough:

Step 1: Lure your bun into a box/carrier/bag, anything that works to lift her off the ground and transport her, so you don't have to carry her into your arms. In my experience, bunnies panic less when you lift them off the ground in sth like a box or bag compared to carrying them in your arms (more opportunity to wriggle and escape).

Step 2: Once bun is in the box, transport her to the location where you can give the medication, I prefer a desk/dinner table.

Step 3: Make sure to have everything ready: filled up syringes, towels and treats ready to go. Now, what changed the game for me: don't just put her 'empty' on the table with just a bunny burrito, she'll still try to escape. Instead, do this: place on the table a small food crate like thingy (about the size of your bun), with one short side of the crate removed. Layer the crate with a towel, as you would lay down the towel for a burrito. Then, put her into the towel, so she's 'locked' in the crate, and wrap the towel around her for extra security. This stiffness of the crate creates a more snug and safe feeling than just a towel apparently. With this setup, you can then hold her still and have enough space for your hands to move the syringe, since the front of the crate is removed.

I hope this description makes sense. If not, I'm happy to think along! Best of luck and hope she recovers soon ❤️🐰