Sleep Machine Connection

In the MFP phone/tablet app, you can get a full list of the devices/apps with which MFP has connections (partner relationships). It's in the "More" menu under "Apps & Devices". On web browser MFP, this would be the direct browser link: https://www.myfitnesspal.com/apps

Sleep integration with MFP is fairly new. AFAIK, the only sleep integration currently is through Google Health Connect. However, Health Connect is able to connect with various other devices/apps.

I don't know whether Dream Mapper is on MFP's list, or can connect through Google Connect, but those are possibilities you can explore.

(P.S. I don't work for MFP, I'm just a regular user like you, trying to help you narrow down an answer since no one with more knowledge has replied to your post yet. Personally, I ignore sleep tracking, because I know that my Garmin's sleep tracking is very, very inaccurate for me as compared with results of in-hospital-facility sleep studies. I don't expect better results from other alternatives, at this point in the technology's maturity. Yours may work fine for you - this is just me.)