if you want to handle only one or a few accounts and this is the only task you want to perform, you can easily record a macro w/ iMacros, to prevent the continuous logging in and out, tie one firefox profile to each twitter account and run separate firefox instances, that way you don't need to worry about the cookies either, you can load the tweets from a .csv or write well spun comment and submit it to a free online spinner (iMacros doesn't support spintax itself), incorporate this into the macro, extract the result and post that on twitter, use "WAIT SECONDS" to schedule the tweets and play the macro in loop, iMacros even has proxy support (private proxies w/ ip auth)
it's not web-based, but if you can put this together and i can't see why not, it'd be a real set and forget stuff completely free (until twitter doesn't change something lol)