Tbh honest Op, i think the whole i'm busy/booked up thing is a load of nonsense. You make time for the people you want to see. If they are as booked as they say, that tells me that you were not on their radar of people to make arrangements with initially.
I had a friend like this yrs ago. I asked her at the very beginning of a new yr if she was free for coffee ( i had recently lost my Dad and just wanted to be busy and distracted really with something to look forward to.) She rattled off months of plans but was free April 6th ( 4 mths later). I " booked " it in and then 2 days before we were due to meet she cancelled by txt saying " i cannot afford to meet as i have spent so much so far this yr , i cannot afford it". I offered to pay for her coffee ( less than £5 no big deal) to which she then replied she "was very tired from all her busy weekends". She then suggested an alternative date in the August. I replied with " I need to check my diary and come back to you" which she would have known was me being sarcastic, but i never did! Have not heard from her since either. That was 3 yrs and i was a very good friend to her helping her out often, supporting her etc.
My point is people will make time for those they want to see. All this booking months in advance is total rubbish, they are booked up yes, with the people THEY want to see or doing things THEY want to do. Fair enough, just do not make yourself so avail for them , when they find themselves at a lose end.
Try to widen and increase your circle of friends op and then you stand more chance of being someone's priority. If you hardly see this friend and then when you try to, you have to pencil yourself months in advance, that is not a friendship. I hope you find someone to go to the thing you want to do with, so you don't miss out.