How do I convert DMs into subscriptions?

I just recently started an AI „influencer“ and got some good traction. I consistently get target audience DMs on Tiktok but not on IG. My Tiktok message requests sit at 100+ because I‘m not sure how to efficiently get them to fanvue, since tiktok bans these links, even if they’re not direct via beacons or linktree. I tried somewhat of a funnel before, where I send them to my Instagram first, chat for 3-5 messages, go silent for a day and finally point towards the link within my story highlight with a „I‘m always active here“ type message. So far I‘ve gained a single fanvue subscription out of some 25 chats. I want to know if there’s a better way. Content + Fanvue is automated, I just need to build the bridge between followers and paying customers. Has anyone faced similar startup struggles and might be willing to share a thing or two? Would come in handy. cheers.