Reassurance is really important, but as far as i can see i think you are doing your best to do so. Her problem sounds typically bpd-ish, her need for reassurance is "out of control". I was in a similar situation (with me being in the position of your friend Jane) and I think it is most important to establish some rules to play by, therefore you should have a conversation with her. Tell her what she means to you, tell her you will be there for her, maybe let her know that if you don't answer the phone or text her right back you are busy, but you PROMISE (and you gotta keep that promise in order to make it work) to get in touch with her at least once or twice a day or how often you think is suitable for you. It might be tricky and seem a little silly and it will surely be a challenge for your friend as well, but eventually she will learn how to handle it and she gets something to hold on to bc she can be sure you will at least text her at certain times (of course you can still text even more or call her or whatever you guys do, this is just the minimum). Let her know it's not to set any limits to your relationship but to make it more stable, oh and give her lots of reassurance after telling her, I am sure she needs it.

Another thing that worked for me was when my friend asked me to make "counter assumptions". That means you could ask Jane to make a contrary assumption while her mind is in overdrive worrying heavily why you aren't replying. For example:

Let's assume she texted you but you are studying heavily for an exam. Her assumption will probably be "he does not want to talk to me, he hates me, he is leaving me" and that will drive her nuts. In that case her job is to make a counter assumption such as "he wants to talk to me but he is probably busy, he likes me and he wont leave me he just has no way of reaching out to me at the moment". She should actively think about it or even write it down, it will help calming her a bit until you have the time to get back to her.