I don't really have a suggestion on the soldering iron.
But I found for soldering the psram chips to the beta/regular Teensy 4.1 and flash chips to the Teensy 4.1s, to the audio shields, and to SOIC8 adapters, that getting a thinner version of the Kester solder really helps. I normally use a Kester 0.031" solder, but for the surface mount chips I found a 0.020" solder. I picked mine up at a local electronics store (probably You-do-it in Needham, MA, USA or maybe Electronics Plus in Littleton, MA, USA), but looking at Amazon I see:
One thing that I found is helpful is having a count-down timer. Every so often I would get up and forget to turn off the soldering iron. There are some irons with motion sensors that turn themselves off if you don't use them for awhile. If you don't have a soldering iron that turns itself off, then units like this can insure you don't leave the soldering iron on for hours. Note, I have the older version with separate buttons for each amount of time (15 minutes, 30 minutes, etc.). The new version looks like you have to press a button several times to select the appropriate amount of time:
I bought this Velleman de-solder pump with heater that works better than the normal solder sucker to pull up solder. That is because you need to hold the soldering iron in one hand, and a manual solder sucker in another. With the Velleman, you can hold the tool in one hand (with a finger on the pump button), and your your other hand to stabilize the chips. One thing that I wish the Velleman had was a light to indicate it is powered, and a separate switch to turn it off without unplugging it. I bought it at my local Microcenter, but it appears Microcenter may not carry it any more. In my experience, it works better on removing solder from pins, while the normal solder wick works better for things like flash memory chips:
As I've posted before, my method is not the method others use. That method appears to be putting solder on the pad and then heating it up so it melts, and using the iron to break the connection).
Instead, I carefully place the chip so each leg is centered in the pads. I attach the chip with either a piece of clear tape (i.e. Scotch [tm] tape) on one side, or use an alligator clip to hold it in place. I start with the iron on the leg and use the thin solder to draw out a line. I do not put solder underneath the legs, but instead have the solder form a bridge from the legs to the pads. After doing one side, I remove the tape or alligator clip and work on the other side. I make sure there are no shorts between the separate pads with a voltage meter in connection mode (i.e. a buzzer rings if the ground/power wires are connected electrically). Make sure you have plenty of solder wick available. I think I've had to redo one or two connections on each memory chip.
On the Teensy 4.1, I attach the memory chips first before attaching the male, female, or stacking headers.