Something that might be a useful combination of the hoisting and the basket over the pot, is what I usually do.
That is, just hang it from a hook over the pot. You pull the bag by hand as usual, and as the OP would have to anyway if he wanted to put it in a separate basket... But instead of going in a container of some description, it just gets hung off a hook, or off a nail in a beam or whatever... Preferably above the kettle and with the very bottom of the bag touching the surface of the wort to stop splashing... As pat described.
Truly, on a single batch,
Even with a fairly large grain bill, the bag just should
not be very heavy... I honestly think that if your bag is particularly heavy, even when you first lift it.... Then you are perhaps using a less than ideal version of the fabric. At the G&G demos we do occasionally... I always answer the "Jeez, how heavy is that bag?" questions by lifting and holding the bag by hand... with one hand only. Now i'm a tubby bloke at only 5 foot 9 & if I can do it with one hand, I really can't see how the "heaviness" of the bag can possibly be an issue for anyone who doesn't have a physical impairment of some description.
A hook, or indeed a pulley, addresses pretty much all the pertinent issues. It allows the bag to drain, allows squeezing, allows this to happen over the pot as it is being raised to the boil - without requiring a vessel or basket as additional gear, which needs to be cleaned, stored, purchased etc.
What it doesn't do is allow for easy sparging, but my point of view on sparging BIAB brews is fairly well known. So if you have sparging as a
primary reason for deciding on which method to use, I have little faith in your ability to distinguish common sense from dross anyway, so just ignore me and save us not the trouble.
I hate to sound like an "old hand" who just wants newer brewers to take whatever they say on faith... But if you go back through the relevant BIAB development threads... Pretty much all this sort of stuff was thought of and tried out before the common paradigm of pot, bag & pulley was arrived at. There are good reasons why they were't the processes that ended up being adopted as the standard.
Now I'm not saying that a lot of these things (even sparging) are wrong, bad or don't work... They aren't and they do generally work... It's just that in general, they add to the complexity of process and equipment, take away from the simplicity and in return, add very little of benefit to the end result in the way of ease or quality.
Hook off a bit of rope is as complex as it needs to be... Why would you want to make it more than that? Mind you if you
do actually want to make it more complex than that, I think that's fine too... But if you are just looking for an effective solution - Then thats been done already.
TB