As far as keeping receipts- Many health insurance companies keep track of your records online and you should have easy access when needed. If your insurance company does not do this currently, it will be coming shortly, and you will definitely not be needing to rely on paper receipts for the next 50 years.
Also, if you use a debit/credit card to pay for the purchase, it is tracked there as well. This may not be enough of a "record," but you will at least know what you paid and when you paid it so it can be easier to track down.
I have posted on this before, but for me I think it is easier to just use the HSA how it was intended. Keep in mind, HSA administrators have somewhat high fees and require you to keep a minimum balance before investing, which detract somewhat from the appeal of spending after tax dollars to keep money in the HSA. Personally, I max the HSA out every year and invest what I have over the minimum balance. The amount you have invested is still "invested like a retirement account" like the OP stated as long as you don't spend every dollar you put in each year. When I have healthcare expenditures, I spend it out of the HSA.