This transmission is probably one of the most robust that Volvo has used however even though this is the first post I've seen for a failing AW 30/40LE, my own transmission on my 93 960 went after having insufficient fluid for about 3,000 miles. (it slipped and wouldn't drive)
Toyota has used the same A341E on the Lexus LS400 and Soarers with great success and is probably the same transmission with a different bell housing and a change in some sensors. Gear ratios would be similar. If you pull the transmission and try some Toyota salvage yards, you may find it's the same unit. This could save some dollars. In my case I paid around $1,100 fitted at a Volvo specialist. Please let us all know how you went. There aren't many 960 forum members here but the ones who log in regularly would love to know how it went.
Current cars: 1995 850, 2000 V70 non turbo, 2001 V70 XC project, 2002 XC70
What we used to own:1987 740 sedan, 2002 S60AWD, 1989 740 turbo wagon, 1985 760 V6, 1995 850 wagon, 1999 V70 project car.
In forum posts please call me Mike