open the .txn file using any text editor on your mobile, copy its content then load it on Electrum by clicking the paste button. It worked for me.
That is a very nice (and somewhat undocumented) feature... thanks for sharing!
So I guess the only option is to broadcast it using coinb.in
As above, you can follow khaled0111's tip and just "copy" the raw hex using a text editor on your Android device, and then in Electrum Android, on the "Send" tab... click the "paste" icon... it'll give you a preview of the signed transaction and the option to broadcast