So is there any way to store a master password online, encrypted, without having to remember another password?
I don't think that is possible.
However, if I were in your situation, I would choose what I will call a "pass sentence" that is easy for you to remember, rather than a diceware password.
In theory, that has less entropy than a diceware password. After all, someone who knows you as well as you know yourself, will almost certainly be able to guess it. So you need to pick something from long ago in your life for best safety. And of course you must protect yourself from shoulder-surfing (always a good idea anyway).
An example, loosely paraphrased from something similar I often use, is "When I was 12, I drove a car into a tree." (yes, including the comma and the period at the end). I also had a mnemonic on paper: "W* 99, I d*." which reminded me that the first word was capitalised, there was a comma after 2 digits, and a period at the end, because in the long run those are the things you will forget. (The "d" is there because I once found myself remembering it as "I ran a car into a tree" and sweated bricks until I calmed the hell down and remembered it was drove not ran!)
Needless to say the above example is not what I actually use, but it illustrates what I want to say reasonably well.
You'll find a lot of password examples that advocate something like this, but shortened to first letters of each word. Resist the temptation to do that. Size does matter :-)