How exactly do you get it to keep going? Every time I try a prompt like this in the playground it spits out a couple paragraphs and then refuses to generate anything further, even with tokens maxed out.
You can also tell it "Continue, but with (...)" to fine-tune the output further, or "Tell that again, but with (...)" to adjust the previous response.
I found that "continue exactly where you left off" will continue in a way that you expect it to more often.
I never used the OpenAI playground, see if Poe.com will work for you. They give free access to GPT3.5 and Claude, Antrhopic AIs competitor. Paid subscription for GPT4 and Claude+
You can just resubmit the prompt and existing history to have the model continue generating new tokens.