How to get from Sheki to Tbilisi

Wikitravel's article on Sheki (aka Shaki) seems to make it at least somewhat clear:

(Balakan is the border town, about 12km from the crossing with Georgia.)

• By taxi: A taxi is also a fine, if more expensive, way to get to Georgia, and you should have no trouble finding a taxi, bus, or marshrutka onward from the border at Lagodekhi to Tbilisi.
• By Minibus (Marshrutka): Bus/minibus departure times from the Sheki terminal: Balakan: 10:10AM, 2PM..
• By train: The train station has a somewhat inconvenient location of about 17 km (11 mi) from the city center... Daily departure times from the Sheki terminal: Balakan: ~6:30AM

This strongly implies there is no direct bus - but is not a definitive answer either.

Another bit of information lacking is whether the train to Balakan continues on to Tbilisi or whether you would at least have to change trains. But since we know there is definitely a train between Baku and Tbilisi I would expect you can take the one train the whole way, or at least there would be a standard connection for the rest of the way since there seems to be only one train per day.

I'm going to update the above info with costs + time breakdowns.

1. Minibus from Sheki Bus Station to random corner in Balakan. 3.50 Manat. 10:10 AM and 2:00 PM. 2.5 hours.

Note: Find the bus to Balakan--it will be clearly marked--get on, and pay the driver at the end. It filled up. Try to get on a little early.

2. Taxi from Balakan to border. Around 3-5 Manat. All day. 15-20 minutes.

Note: They will almost certainly try to rip you off. The guy told me 6 and charged me 8 at the border after I gave him a 10.

3. Cross the border. 20 minutes.

Note: Make sure you have your Azerbaijan visa with you. They asked for it on two occasions.

4. Exchange $$ or Manat for Lari. I don't recall seeing ATMs, so keep some extras.

5. Minibus from border to Lagodekhi. All day/frequent. 2 Lari. 20-30 minutes.

Note: You can find the buses pretty easily. They are very easy and certainly cost less than the taxi option.

6. Bus from Lagodekhi to Tbilisi. Frequent. 7 Lari. 2.5 Hours.

Note: The last stop is right next to a metro station called Grmagele.