Speaking as someone who spends too much time sorting out BT problems, I don’t think we’re going to be able to support OBEX - it’s a bit niche.
Can I suggest you just take a SD card or USB stick when you go away?
You do know you can play music from a phone to OSMC using BT audio? Atm it’s not installed by default. See here
For your use, you don’t have to mess with the .asoundrc file, you should just be able to install the package, pair the phone with your OSMC device and select it as output on your phone.