The automatic transmission in my 1994 E34 525i went out at 145,000 miles. Same exact sympthoms as yours. None of the local bmw independent repair shops wanted to rebuild it; they only were willing to install a rebuilt tranny from BMW, which was about $2000 alone, plus the indys wanted about $1000 for r/r. I finally got a local transmission place that specialized in german cars to do it. When it was apart, they called me and asked me to visit. Between several of the gears, there are suppose to be plastic washers called thrust washers. Mine were gone, either having gotten brittle and breaking, or possibly melted.
Cost of rebuild, including several gears and one sensor was $2200, including labor.
By the way, now I drain and refill the automatic transmisson fluid (without removing the pan) every time I chg the engine oil.