Been googling this and until your post, I've read the e39's automatic box (and thus its cooler) is up to the job....
From what I've read, the trick is to not to allow it to labour in lower gears in D mode,more use it in S and use the steptronic for hills to hold lower gears.....
Looking at twin plug but probably not a detachable tow bar as they do cost a fair bit more, . I've found a second hand tow bar suitable e39 Sport bumper though, different colour to mine (typically) £200, which is the price difference between the detachable ones and not, so, . It's a non detachable for ~ £250 or, circa £650 for detachable and suitable bumper, a bit steep on car that stands me £1500 I think.