I know what I say won't make any difference to you at this point in time, but given I know you, her and of your friend, I feel I can confidently help to reassure you that you're not going to lose her any time soon. Yes, there was that one scare, and thankfully I was watching, but that's one little slip she had out of countless days and nights since you brought her home. It doesn't necessarily mean anything's going to happen to her again, or more often, and further, just because that happened to your friend (pretty sure I know which one), doesn't mean it will happen to you. You have to remember that.
You have a very happy and healthy bunny who is thriving right now. The only thing she will need in time that you're not giving her (or are yet able to give her) is more space/freedom, but you're doing the best you can with what space you have, and in your free time, you're giving her even more space in a larger area, while supervised. She loves and adores you for that. She's perfectly healthy as she is and you take amazing care of her - even putting her own needs above yours sometimes, which, as you know, I was never too keen on, as you being around to look after her is more important, but that alone shows the love you have for her and she will feel that. She's bloody spoiled too with the amount of treats and toys you get her!
If you're particularly concerned though, my suggestion (with whatever weight my opinion may carry with you at this time) would be to at least get her checked out at that place we looked at. If they can check her out, they can reassure you further and let you know how else you can best help her or take better care of her. You know you need to get her fixed at some point soon as well, and that will help ensure her continued good health, since you know the risks of not doing it.
Beyond that, you just need to keep caring for her as best you can, and when you're at work, do your best to trust those you live with to check-in on her every so often. Maybe your sister could be more involved? - now that she knows she's able to help out in an emergency! Your mom does make sure she's okay when you're not there, even if she's a bit hapless sometimes - she does at least try, and honestly, all that's needed is someone to keep an eye on her and make sure she's eating/drinking fine while you're gone. She has plenty of toys and things to keep her occupied while you're out too. You know from my recent running commentary just how much fun and excitement she enjoys!
She's doing absolutely fine and you're doing brilliant with her. You're not in any danger right now of anything horrible happening to her, so it needn't be a worry. I know you'll always worry about it and you can't help that, but try your best to push it to the back of your mind and enjoy the time you do have with her. You've only had her for a year and a bit. She's going to live for a long time if you continue the level of care you have. As I said, the only thing she will need eventually is more space to run around and play in, but that will come in due course.
Another thing you could do is maybe research vets who do call-outs? or mobile vets? They do exist, I'm sure. Either way, the place we looked at, you and I both know will take good care of her if need be and it's not TOO far out of the way, though of course, it would be preferable to have somewhere closer. Keep an eye on things and keep looking to see if somewhere opens up in time? It's always worth keeping an eye out for these things.
With regard to picking up on her illnesses quickly enough, try to remember when you did that previously. Try to remind yourself that you HAVE done that before. You took action straight away and pre-empted anything worse happening... and what happened? She went straight back to being her usual giddy self and gave you all the thankful loves for helping! Just remember the good you do and how well you have taken care of her in the past, if you ever question whether you will in the future. Of course you will! I suppose the other thing you could do is create a second Skype account (or whatever) and call your computer from your new phone (when it comes) and watch her on the webcam while you're at work. That way you can always keep an eye on her? It's a bit fiddly to do, and of course, you'll need to use your data plan to do that - unless you can persuade your mom or sister to answer the call once you get to work so you can use wifi instead - but it's do-able and I know you can handle that.
I'm sorry your friend had to go through that though... It's awful and heart-breaking, especially knowing she was there for those last few moments, but I'm also sure knowing she was there and got to say goodbye will help her heal in time. I'm sure you did your best to help and comfort her, like you are always so awesome at doing. It's going to be tough for her, but I'm sure you'll be there to support her, and maybe seeing her go through that process will help prepare you for if/when the day comes - years from now...? I dunno…
I hope that helps somewhat and reassures you that you're doing a great job... She's a very much loved (and missed) little bun and she knows it! She's not goin' anywhere any time soon! Too much banana to nom on!