The hard carve upwind is a maneuver used by many sailors to slow down at the end of a run in toward the beach, and yes, calling it a carve tack is about correct.
Next time, just quick step over the mast, keep the board carving/planing and sail off back out to sea. First time I saw some top level sailors doing planing tacks I was astonished! Took me a while to figure out exactly what they were doing.
On your raking the rig back issues, if the board is turning upwind when you do this you do not have enough speed to be doing it.
And I would guess that as you are doing it you are somehow shifting a bit more weight onto your outboard front foot, or onto the heel of your back foot.
The rig does get fully raked back until the foot angle is parallel with the deck of your board (maybe even touching your board at the back on bigger sails) but you cannot do this until you are hooked in and fully planing at nearly top speed.
You need lots of apparent windspeed to make fully raking the rig back work, so wait a bit more when raking the rig.
It's more powerful standing up slightly, but gives you better speed raked back to allow you to sail on apparent wind.
You really need to be in both footstraps and really moving before the rig gets fully raked back and sheeted in to almost the centerline of your board for sailing upwind.
If your course is further off the wind, you may not need to rake back or sheet in quite so much unless you are on formula gear that sails almost completely on apparent wind.
You can also "footsteer" once you are in both footstraps.
More pressure over the top of the fin with your back leg (towards downwind) takes you upwind more.
Backing off the pressure on your back leg and rolling the toes on both feet down a little will take you off the wind. It's not intuitive.....you'll figure it out, just like your carving tack.
Hope this helps,