Welcome to Flyertalk!
LHR-LAX was one of my regular journeys when I had family living 20 minutes up the A40 from Heathrow. Actually I find transpolar flights tend to be smoother than shorter ones, as they spend so much of their time at higher altitudes.
Irrational fears are not always soothed to hear rational answers, but if it helps to know:
• road traffic in London or Los Angeles is thousands of times riskier than nonstop flight between them
• it's the
job of the pilot you chatted with to know all possible perils of what he does in order to avoid them, but he may go an entire career without ever encountering many (He might have spared you if he knew it was upsetting, but most likely finds it fascinating himself.)
• modern aircraft are among the most dependable vehicles ever made; they are overbuilt for what they do, and serviced by highly-qualified careerists
Keep your seatbelt on whenever seated; it need not be take-off snug for the entire flight. If looking out a window doesn't aggravate your worries, you may enjoy spectacular views of Greenland, Hudson Bay and the Canadian Rockies. On one flight we even got to see Comet McNaught, a sight denied to many on the ground who would have liked to.
Oh, and on-board duty-free items are often NOT a bargain!
Congratulations on the progress you've already made, with best wishes for continued success.