As far as my Agilent U1272A is concerned - there is no problem:
APo = off
blit = off
...no problem at all to stay on with backlight on till the end of battery life:
The same applies to the U1233A and the U1273A without the need of having "blit off", because of OLED!
As far as my Fluke 113, 117, 179, 87V is concerned: in "MinMax" mode they also do not power off. Therefore you can use the "power up option" "Loff" and you have "nearly" the same...
Cheers!