I think your first approach will work well.
mash in the esky, then drain into the kettle. I have done this a couple of times for larger batches before I built my 3v with herms.
Put about 5 litres less the required volume of water in the esky (about 5 degrees above desired strike temp), bang on the lid and leave for about 5-10 minutes. This will kind of pre-heat your esky and you will lose less temp over the mash period.
Once at strike temp, pop in the sheet, then grain, good stir, re-check temp, top up with the 5 litres hot or cold water to bring to mash temp, bang the lid on again. cover with a blanket and leave for an hour. (check it at half time if you really want to and give it a bit of a stir, but you will just lose more temp).
Once mash is finished, give it a good stir, let sit for a couple of minutes. Leave the grain in the esky with the bag and slowly drain a couple of litres out. gently pour this back in not to stir up the liquid (vorlauf). This is a full volume mash, the grain bed will not compact as well as a normal mash, it will easily stir up with the liquid you pour back in - you don't have to do this step, but it just helps for a little bit clearer wort.
Slowly drain into your kettle and start to boil. You can always pour some hot water (80-85 degree) over the drained grain to get a bit more volume into the kettle if you are short.
Looking at your kettle, I would not try to BIAB in there because when pulling the bag (or the square in your case), it will literally go pear shaped and be very hard to squeeze though the top and you will have wort running down the sides of the keg. - Been there, done that!
Hope it all makes sense.
All in all, this will be your first attempt, so don't stress, get to know your gear and change your process to suit you.
Cheers,
Hammo.