always remember that you are the one who is paying so you must remain the boss
A GP doc will usually prescribe the meds you get from the psych
I understand you feeling the time pressure of all the things you have going on right now. However, this really isn't a good time for you to sacrifice your therapy time. The holiday season is stressful enough, but adding a home relocation and a new job on top of it, dropping your therapy support system, even if a little sketchy, is probably not a very good idea to make it through this transition with your sanity intact.
Feeling guilty about having to cancel an appointment, indicates that you put your therapist's "feelings" before your own. A therapist is a professional, their "feelings" are irrelavant. Appointments in any professional field need to be cancelled on occasion. Things happen, that's just the way it is. However, you need to realize that if you have a standing appointment day/time, to cancel this for an extended period of time leaves an opening that a therapist my very well fill with a new patient. Expecting to get your time slot back probably isn't likely to happen, as it has been filled by someone else. If you stay with the same therapist, you may have to take whatever appointment time is available. This very well may not be convenient with your new job.
By your description of your therapist, I would definitely look for a new one after things settle down, after the first of the year. If a therapist mentioned that they might be seen as "judgemental", they probably are and you should dump them immediately. You should always feel comfortable being able to talk about any subject with your therapist, without the fear of what your therapist might think. A good therapist should be able to give you suggestions on coping mechanisms, not critiques or criticisms. See if you can get a recommendation from your physician and give them a shot. It may take a while to find a therapist that is the right "fit".
GOOD LUCK. Let us know you are doing.