That is very strange. Something is not right, as you say.
In my mind, there's really only one of two possible answers: a software issue or a hardware problem with the flight board. Here's what we "know":
* You've calibrated the ESC's with the calibration build of MW.
* You've modified the config.h with a valid MIDRC and MINTHROTTLE for your setup (DX5e, ESC's, motors)
* You've erased the EEPROM, and reflashed with the correct MW23 build for the DX5e
* You've been able to fly about a minute with just a persistent forward drift in the past
* No hardware changes, have verified motor directions and commands to appropriate motors
* Two motors/ESC pairs are behaving as expected on bench, two are not
What I know of motors/ESC's are: ESC"s and Motors have a voltage level based feedback to each other. ESC"s and flight controllers/RX's are generally unidirectional PWM signal based (RX/Flight board -> ESC). So, what you're seeing on the MultiWiiConf (PWM rates being sent to the ESC's/motors) is based only on sensor feedback to the software running on the board and your RC input commands.
I didn't think it was necessary, but perhaps even with MW2.3, despite being in Acro/Rate mode, you need to recalibrate the ACC after a EEPROM erase. You can use the stick commands to do so (Low throttle, full left yaw + full pitch back):
https://multiwii.googlecode.com/svn...tiWii-StickConfiguration-23_v0-5772156649.pdf
Do that while the quad is level and perfectly still. In fact, you might even recalibrate the gyros if you want before re-running those tests above.
If that doesn't work to resolve it, here's another shot in the dark (trying to remove, somewhat by brute force, some of the software variables):
I've taken the liberty of merging your MW23 DX5e Quad config with MW2.4:
https://dl.dropboxusercontent.com/u/25601637/MultiWii24_FTSpiderQuadDX5e.zip
I'm not sure why this would make a difference, as it's more of a shot in the dark, but I'm at a loss for other software options.
Just check that the MIDRC and MINTHROTTLE is ok for you. I reset what you had for MINTHROTTLE with your latest test result from above (bumping it up a bit more).
One other thing: with this build, you WILL need to use Arduino 1.6.1 (the latest) SDK from
http://arduino.cc/en/Main/Software
It will result in a smaller binary file/hex file that's uploaded to the board, due to some fairly major libraries changes... so, you're not only updating the MultiWii codebase, but also the shared libraries / build environment...
Definitely do the EEPROM erase (from the new Arduino IDE) before flashing MW2.4, and recalibrate the ACC afterwards. You may notice after this, that in MultiWiiConf, it'll look like you have a compass... you still don't, but the quad might rotate around the compass because it's trying to calculate it in software.