First - :hug::hug::hug::hug::hug: , if accepted. I'm so very sorry for what you are going through.
I am on my own as well and have been living hand-to-mouth since 2009 when I was laid off. I can relate to your reticence in leaving your position in regard to income and insurance. Money seems to make the world go 'round and when you don't have then it seems the bus hits the brick wall. It brings on a lot of fear when there seems to be no net to catch us.
From what you've written, it seems that you do want to make a change in June and are just trying to make it through until that time, but are also afraid of the financial/insurance implications of working part-time. If so, it's time to mentally strategize as best you can.
If you have an employee/union handbook, look at it to see if you will qualify for insurance. Next step, consider looking at other pools for insurance - professional organizations you might belong to or can join, COBRA from employer/union (not sure if this can apply when you cut back to PT hrs (check HIPAA regulations)??
Worst case scenario - keep an eye on the ACA mandate situation and requirements attendant to that. You can check eligibility online and not deal with the call center - I highly recommend this route. If insurance won't be available to you with PT hours, work with your T to seek out alternatives that might include transitioning to another T who works with a sliding scale. You'll need time with your current T to help you with this transition, especially if you've been working with him/her a long time. Also, get all of your medical up to speed - any MD appts, labs, diagnostics, Rx that you might need for months past June? Pick-up the Rx 90 refills just before your insurance expires. I did this and it has been helpful.
Also, take time to build up self-resources such as self-care and compassion. Get that regimen set if you don't already have it in place. Also, figure out what stabilizes and/or you - nature, mindfulness, spiritual pursuits, creative activities, music/art, writing, walking/yoga?
The other issue - income. What about a part-time job doing what you like and that you find "fun" to pair up with your part-time day job? You'd still have income, though just not as much and it would be less stressful. I've been working on this. Will probably get the part-time before the day job, but it's a start. Also, know that some employers offer benefits to part-time employees working 20-25 hrs. Starbucks is one that offers insurance and tuition costs. I believe Whole Foods, Home Depot, Target, and a few others do as well. Google that.
Perhaps, a SWOT analysis on your life might help you to prioritize and comfort yourself. Strengths, weaknesses, opportunities and threats. Get into Excel and just belt this out. I did it and it's amazing how many opportunities you'll add over the course of a week and also how many strengths you have that you may not automatically think of.
All this to say, in preparing for what you see as inevitable, you are identifying and shoring up your resources, and reassuring yourself that you're not going to be falling into the abyss. You're just taking another path at this point, one that you feel is needed. It's not an all-or-nothing proposition for you, but a side-step. Just do some thinking through and planning. You might be surprised at what you determine after an analysis of your situation.
Praying for you. VB