Possible; I'd rather just have the two measurements we've got now, and a %, but I think they're trying to avoid stating a %, because some people don't get the lack of precision in measuring state-of-charge on a battery under load, and would get confused...

Not appreciably. The computations there are negligible. I've got 6 hours uptime, and the bme has taken a total of 5.11 seconds of computation.

It's not that bad, I don't think. Edit your (presumably stock) /etc/mce/mce.ini, and set doublepress to softpoweroff. (And set longpress to do nothing... not necessary, but prevents inadvertent shutdowns.)
Now it's a double-click to softpoweroff. Then a longpress powers back on, and the dpad-select button unlocks. (This is my favored config...)

You can also get things working with longpress, but this worked best for me after I reduced the long-hold time to 1000 ms; also, you have funny business with the screen flashing back on, then off. Wierd. But, it does work; longpress for softpoweroff, on release, it flashes the screen and then goes out. To wake it, do a longpress, and then hit select.

Tips:

• I've only tested this with the dim and sleep timeouts identical; in old versions at least, there was strange behavior when these were different. (Like keeping the screen on until the difference between them elapsed...)
• It needs a longpress; the screen comes back on immediately, and displays "Now press [o]", but keep holding on to come out of offline. Then hit select.