Most people I know on Facebook just link the people over to their Tapas episode to circumvent this problem.
So one way to only have to export things once would be to link everything to your Tapas, but still advertise your comic on your other accounts.
Tapas and Instagram seem pretty compatible with each other in terms of formatting, so you could use the same file for both of those sites (and I think Tumblr too, but I don't use Tumblr that much, so I can't say for sure). Facebook really wasn't designed for comics, so if you really don't want to export the same file multiple times, you could use Facebook to advertise your comic but not actually post your comic on it.
In conclusion, use your Facebook to link people over to other sites instead to use one file for your other accounts.