Fixmystreet needs a commitment from the local authority
This sounds like you guys covered a lot of of ground, more power to you!
Out of all the points you made, I would like to throw in my two cents, or rather my two Tetri (cool name by the way) on the mobile app for fixing the streets proposed by @Mamaduka. Technically this is not too difficult to build. The source code for the rock-solid FixMyStreet is open, and the nice MySociety people in the UK will be delighted to help you set up a Georgian version. Here on Edgeryders, Italian hacker @piersoft built his own Matera Pulita (Clean Matera – Matera is the name of the city where he is from): he is a very generous person, and I am sure will be happy to help you. But make no mistake: behind the app stands a social contract, and that social contract says that if citizens spend time uploading a request for the local authority to fix the street, they have to come down and fix the street. If this does not happen, citizens become frustrated and stop using the app (rightly). For the app to work, you need to secure a firm commitment of the authority in charge of fixing the street before you launch.
In fact, I recall an experience made by UNDP Montenegro that made exactly that mistake. They built the app, and initially people used it. But then, guess what: in Montenegro, responsibility for street maintenance lies with municipalities (in Italy, too). But municipalities have no money at all, they are stretched very thin. So, the sudden rise in expectations induced by the app put them through a lot of stress, and there was some conflict between the national authorities (who had helped UNDP in this) and the local ones (who found themselves saddled with the pressure and deprived of the resources to respond. It did not go well: they had to abandon the scheme, amidst citizen disenchantment. It turns out it is easier to build a mobile app than to change the balance of power between central and local government!
What is the situation like in Georgia? Who is the authority responsible for road maintenance? Would they be willing to do a prototype, committing to responding to citizen input at least in one or two towns?