Currently no, barring exploiting vulnerabilities on the platform (which DJI are pretty quick at fixing) there is no way around the distance limit. The wide field really won't be your issue here. At 60m you can't see it safely line of sight.
Why not get a cheap phone just for this purpose? Doesn't need to be fully featured, or indeed that current - just ...
The maximum altitude is 3000m (about 9800 ft.)
(Note that this is relative to mean sea level, not the ground.)
DJI Mavic Mini "Specs" page (under "Max Takeoff Altitude")
DJI Mavic Mini "FAQ" page (under "Propulsion" > "What is Mavic Mini's maximum service ceiling?")
After a bit of research it seems like the problem is likely to be that you don't have the latest version of the DJI fly app. As per this forum thread you will need version 1.2.4 or later to see the option for 2.7k 60fps.
On android you will need to download the latest APK, while on iOS it can be downloaded from the App Store. Links to both version are ...