in my experience of going down the JR route
you really want to try every other option as the JR will be the lengthest option in front of you as well as being the most expensive.
If you believe your appeal hasn't been lodged within a timely manner (as is still not lodged) then I would
1 - get in touch with the AIT to find out what, if anything has been done
2 - lodge the appeal directly with the AIT.
3 - send emails to the consulate, Ambassador, call up the ambassador's secretary, send faxes, all repeatedly, daily even, be an outright pain, to get them to speed things up/send you and update of why everything is taking so long. You're sometimes told you need to treat the consulate and ECOs gently otherwise they can scrâ‚¬w things up for you. Complete BS. Go in hard, albeit polite, and you'll find you'll get results much quicker
4 - get in touch with your MP asking him/her to find out why the bureaucracy is taking an eternity to get back you.
You need to go down all these routes first before even thinking about the JR.
JR's aren't as difficult, lengthy and impossible as many make them out to be. But they're very tactical and if you/solicitor makes a wrong decision, the whole thing is screwed as I found out.
Having said that, if the appeal is not set in motion within the timeframe set down in policy, then you can start JR proceedings if you have the cash. Most JRs lodged are settled out of court so you might find that simply by starting the JR (which is simply sending a letter to the consulate) threatening them with one (from you solicitor) everything could sort itself out very quickly as they won't want to deal with anything like that.
Try other options first, and if within 2-3 weeks nothing has been done you can revisit the JR route