Yes, you can get some very fine sand paper and ensure each pin is clean and a little shiny. Take care removing the IC. Prise each end a little at a time. Eventually you can get the tool (long flat-blade screwdriver will do) into the middle of the IC. The trick is to lift the IC straight up, rather than lifting one end completely which can bend pins.
As for the II+, try the IIe power supply on the II+ - They are the same pin-outs.
Sadly, there isn't much that a II+ can provide that will help to diagnose the IIe motherboard.
As for easy, the II+ uses mostly "off-the-shelf" ICs, which makes it easier, BUT many of those ICs are no longer stocked by smaller suppliers. The IIe is mostly custom ICs.
Yes, I have to agree that RAM chips are one of the common faults in these machines. Sadly, being all soldered directly, you could end up needing to desolder them all, put sockets in, then test by swapping RAM ICs. - Not impossible, but you'll need some basic soldering skills to do it. Then again, you could do all that, and find it's NOT the RAM.