Nice thing about hash browns is they are kinda good no matter what you do lol. But I'm the same way, I like them well done and real crispy. They turned to mush first time I made them though... Rinsing the starch and drying them is also a good trick to do for homemade French fries. Double frying them is another good trick but might be a bit much for hashbrowns.
You can also blanch the shredded potatoes in hot water, drain very well and fry .