zip up the .lg folder and email it to yourself before you go mobile or when done playing. or google drive or somethign free... plenty of options for a few gigs of space -- significantly less with just 'normal' compression due to the type of files invovled.
hmm, bet you can make it a script to automatically zip and upload to a url etc. modify somethign that may already exist for online leagues?
online storage is easy either way. The 2 license thing is the drawback for that type of use. if steam users can do it, then you should be able to also, imo. take from that what you will. i only speak of the logic, not the means/suggestion to make it so