a customer said my product changed their life and then never wrote a testimonial

last month a user hopped on a call and went on for 20 minutes about how we saved their team. named people. named the old process. said they'd write something that night.
i sent a thank you. waited. nothing.
followed up two days later. "yeah yeah i'll do it this week."
that was 3 weeks ago. i still have the call recording. i still have zero words i can put on the site.

this keeps happening. the people who are happiest are also the busiest. the people who write fast usually send "great product, highly recommend" which is almost useless.
so now i'm stuck between sounding desperate and having a homepage that looks like nobody uses the thing.

what actually works for you when you ask? not the theory. the message you send. or do you just stop asking and live with it.