Hello,
Congratulations on making a post and seeking support and assistance. 
I amongst many others know the pain you’re going through. I have felt overwhelmed, even suicidal, many times over way too much body hair (for my liking), the acne-redness and pain caused by shaving my face often etc. I have spent many many thousands on a variety treatments and probably every gadget/method you can think of.
As many here will say, the only way to go is with electrolysis. Of which I am now doing lots.
Like yourself, laser was not a great option. I mostly have blonde ginger hairs. Nevertheless I have had a lot of IPL and laser done anyway, which has thinned the darkest ginger-brown coarse hairs.
By “thinned” I mean the hairs are still coming back (after 10 treatments over 16 months) but thinnner and weaker than they were. Worse, laser made many of the blonder finer hairs come out darker and thicker - but not dark or coarse enough to be removed by laser!
So I am now doing electrolysis. I wish I had from the start.
By the way, I can affirm that a lot of guys, myself included, find blonde fuzz hair and even darker fuzz absolutely adorable, anywhere, including side burns and other facial areas.
Seriously, I see that on a lady and I go all sheepish ga-ga. It’s like seeing stars in the night sky, or shimmers of light on the water… or something like that! It can be very attractive. It does something to our core.
Anyone who says otherwise, who says negative things, probably has emotional problems and has a hidden agenda to make others feel bad about themselves. So disregard any comments from such people. Maybe feel sorry for them instead 
For they are so miserable and misguided in it that they seek to make others miserable too!
So I hope you can learn to be happy about those hairs, the fuzz, and focus your concern and efforts firstly on any thick darker coarse hairs that people can see ie. maybe electrolysis around mouth areas.
Most of all, focus on the positive things in your life. For we get ourselves into a depressing mental pit by obsessing on negative self-destructive thoughts of “I am not worthy enough to be happy and enjoy life because of these hairs!”
I’ve thought myself into total despair many times like that. And gave up on really living life. But it is rather silly, isn’t it?
The good news is we can do the opposite. Those self-destructive thoughts can be neutralised by choosing to focus on positive things… There are always positive things to think about - pets you love to be with and who love you, family & friends you love to hang out with and who love you, music you love, movies, books, nature, arts, things you’ve achieved or plan to do in future etc.
Make an effort to think about and immerse yourself in those positive thoughts and activities regularly. It makes a huge difference.
Finally, my first long-term girlfriend (and dear friend now) had dark coarse hair up to and above her belly button, hairy arms, fuzz on her face and elsewhere. I recall her telling me she started shaving her legs and arms (!) when she was 10 - though stopped on the arms later. She doesn’t even bother shaving her legs or armpits that often. Though if not she does tend to cover them up when she goes out.
And she has had an absolute ball in life, has had many lovers (all male), she is an exceptionally good lover, she lives life on her own terms and is highly respected and considered very attractive (in the highly-vane fashion industry and clubbing scene!) It’s all because she projects an energy of confidence and of “life is meant to be fun” about herself. And this comes out as genuine great beauty.
I hope this helps you.
with best wishes.
For they are so miserable and misguided in it that they seek to make others miserable too!