I dabble in live production and have been using the Black Magic ATEM switcher for a minute. Its particularly persnickety but if you bring all your sources in at the correct frame rate (23.98 in our case) and size(1080p) through an SDI cable the BM ATEM can be a powerful bit of gear.

I recently purchased 2 OSMOs and I was wondering if by some glitch in the time space continuum it is possible to send out a 23.98 1080p signal to my BM ATEM  from both my 2 different OSMOs while still being able to monitor on iPhones.

not possible as the osmo only sends a wifi signal to a single phone per Osmo, unless DJI make an accessory of some kind, the osmo sends 720p 30fps through wifi

Hi,
Unfortunately, the Osmo doesn't support that feature at present. You may need to resort to your mobile device's functions.
Thanks for your feedback!