I think that you have two separate issues at play here:
1) Your relationship has some issues that need to be addressed if it is to continue
2) It is easy and convenient for you to ignore one another
There is some interaction between those, but it's important to point out that just fixing (2) won't necessarily do anything to help with (1).
It seems clear, from your description of events, that your fiancée is having doubts about your relationship and so is investing less into it. This is your core problem. A lack of communication can make this problem harder to understand, harder to talk through, and harder to resolve, but it is (in my observations of others) far more likely that (1) is causing (2) than the other way around. (2) is very likely to be an indicator of (1). I mention all of this to point out that, while I think it is a good goal to start communicating with each other more, more communication alone will probably not return your relationship to how it used to be.
So, how do you communicate more? I recommend putting the communication into the context of your relationship as it currently stands, accepting that you will probably not be able to reliably communicate with her as much as you prefer, and formalizing your communication schedule (for now).
As scohe001's excellent answer suggests, your fiancée is reevaluating your engagement and your future together. This isn't necessarily a catastrophe-- she may well conclude that she does want to be with you, and having gone through this situation can then let her move towards that confidently and without resentment. But this is a situation that you cannot directly control, and past events and situations do not and cannot enforce any particular outcome. That is to say, her suggesting that you get engaged in no way prevents her from later changing her mind and does not require that she actually marry you.
The current situation is that you now have different goals for your relationship, and determining what you both want and how you can proceed is what you should be talking about. Casual chit-chat about your daily lives is probably not on offer, whether that's what you used to do or not.
Formalized schedules for communication
So she may not be very receptive to you suggesting that you two talk on the phone every single day, simply because for you that is a sign of a relationship as healthy as you want yours to be. By ignoring your calls and texts, she has already demonstrated that she's not interested in this right now. She may be more open to you two talking during a scheduled call once or twice per week. It's less of a burden on her time and attention, any formal arrangement you make is one that she will have agreed to (so you'll have some knowledge of her thoughts), and it's much easier to track whether or not you've talked the agreed-upon number of times in a week vs. whatever amount you feel is "enough".
Less contact than you want
It's very easy to not talk to someone that lives far away: just don't answer the phone, don't respond to texts, and, in more extreme cases, block all communications from that number. Your fiancée can unilaterally enforce zero contact, if that's her preference. You cannot do the same for your preference of more contact.
You've expressed some confusion as to the contradictory things that she's saying, but she isn't really contradicting herself. The most direct interpretation of her comments is that she doesn't think that there is anything especially wrong with you ("any girl would wish to have a guy like you", "she wants to marry you but not now") but that she is not sure that she wants to make this commitment right now.
You would be wise to focus on the meaning of things she has said and done, not looking for what you assume to be a technically correct interpretation of those things. If she wanted, 100% for sure, to marry you, she would not be doing and saying the things she has said and done. Your engagement would have continued without comment. Make no mistake: she is investing at least as much as she currently wants into your relationship; she is not investing far less than she would like for some mysterious reason. Trying to force her to dedicate more than that to your relationship stands a good chance of making her less happy with the relationship, causing her to associate your communications with negative feelings, and as a result terminate the relationship altogether.
My (loose) suggestion for how to initiate regular contacts:
Honey, I know that we've been drifting apart lately, and you seem to be having some doubts about our relationship. But I still love you, and want our relationship to succeed, even if that means that you need some space. Could we set aside some time to talk every week, maybe an hour or so on Wednesdays starting around 8?
I will also recommend apologizing for deliberately ignoring her. It's childish, spiteful, makes it easier for her to justify ignoring you further, and most importantly, intended to upset her, none of which are ideal in a future spouse. I suggest that this take place before and be separate from the request for more communication-- it's a problem, but a side-issue to your more pressing problems.