A high wattage PSW inverter costs big bucks. A MSW inverter can run the hair dryer just as well as the PSW, for a lot less money. Check out the Cobra 7590 eg.
Meanwhile, the electric blanket needs PSW but is low watts.
Price out getting two inverters-- a high wattage MSW (it will also run the microwave-just takes a little longer to heat things up) AND a low wattage PSW (300w Go-Power is popular for that) to run the fussy things like the electric blanket.
You can wire up the big inverter with fat wires and park the small inverter next to it, and run wires from it over to the big inverter's terminals, so that it then shares the same fat wires to the battery.
You can organize which 120v items are powered by which inverter various ways. It is not rocket science.
Might save you a few bucks. Or just splurge on a 2500 or 3000w PSW if you have the money. It all works.
Almot , you can way over-do the Peukert stuff. It only works out if you go all the way down to 10.5 volts (unloaded!) to get the advertised reduced capacity. If you only run a high amp draw for 10 minutes and turn it off, it is like nothing happened hardly --just use the regular AH figure. I have been seeing this on my Trimetric for years and it is just not a problem. It would only show up in real life, if you kept that high load on till the batteries practically go flat.