feline fanatic

That is a pretty difficult block to learn on. I know this block as Tree of Life. Matching up multiple HST like in this block is not easy even for a very seasoned quilter and one who is confident in matching up HST. Which sounds more like the difficulty you are having rather than making the HST themselves.

Tree of life is on my upcoming list of quilts. I did do a sample block in this scrappy flannel and even I had some chopped points in places. My block pattern makes a 10" so I was working with 1.5" HST units that finish at 1" so pretty tiny. Here is a pic and you can see the tree of life block.
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Unless you are planning on entering this quilt in a show, I don't think I would concern myself with a few chopped points. The block lends itself to somewhat camouflaging a few chopped points as it makes such a dramatic statement with all those HST units. As is demonstrated in the above photo. Once all put together and quilted I think you would be hard pressed to find the chopped points. But if you are committed to perfect points for your own quilt here are a few hints:

Well starched fabrics and press will at each step
Glue baste critical intersections.
When joining the triangle squares press your seams open to cut down on the bulk.
Sew slowly when going over the intersecting seams.

Quite honestly, if you are trying to get over a fear of using HST units, I think I would start with something a bit easier using larger units. Maple leaf and Bears Paw are a couple of good ones to practice with. Or something like this quilt which was all HST units that finished at 2". Rather than making a whole quilt you can make placemats or table runners.
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Edited to add, that I do make my HST units oversized and trim down to the correct size, ensuring that my seam line falls exactly on the corner of the HST unit.