Stress, u mean fear that you will soon miss a note, breaking your "sound hearing" concentration for watching notes.
How about going back to easier songs where you was decent, leave your high acc A / S ranks alone and pick decent A / good B, play them with HD (+HR if needed).
Personaly, it stress me a lot while i play HD but to learn control this and do not break my concentration, more, to improve my concentration on song beats and reading, i tend to make "Hidden day" where i play only normal / hard and try to improve my old crappy scores, fc maps while playing only HD mode. After some time i have feeling like "whatever, song will guide me, i don't need to see shit". Funny story - in some songs i made better score while playing HD, strange but if works... why not do this more, i kinda like HD, funny and challenging mode.
With around [Play Count:] 3,934 minus ~600 while i was playing completly cassualy i am starting to reading insane maps and doing better at controling my overall acc.
At the end, i can just say, everyone should develop their own way to bypass stress. Above it's just my personal issue so if you try, it might work or make you worse ^^