Hugs. I understand the frustration. My DD10 also has a number of issues (sensory and anxiety-related) that we have been to different people about, and I so long for _someone_ to put all the pieces together so we can make progress.
DS7 likely has DCD as well as convergence insufficiency. He also also has trouble with cutlery. We did find some nice plastic ones at IKEA that he seems OK with - although still prefers to use his hands.
Re: swimming - been there too! Middle of the last session (with a private swim instructor) she told me she needed to start over and teach him to float. So discouraging! But the current session he's in (group session this time), for some reason he just decided that he was going to learn to put his head underwater - and he did! Spent the whole 1/2 hour dunking himself. I was amazed - it was clearly hard for him - the look on his face every time he did it - he clearly didn't like it (he has some sensory issues). But now he sort of can, and is making progress with the front floats! So - don't lose hope. Sometimes they finally do make progress when you least expect it.
Sorry I have no idea about the compass. DS finally has a good pencil grip after several years of teachers helping him with it. The OT we talked to suggested 'short' pencils, so I also bought a package of golf pencils for home use. They seem to help. I also bought pencil grips to put on them, but he doesn't like them.
I hear you about the expense - OT and vision therapies are not covered by my insurance. Also have paid for years of private swim instruction - it was the only way.
