I believe it was Kevin Voecks (maybe Floyd Toole) who said speaker break in is mostly a myth.
http://www.audioholics.com/loudspeak...ths-and-truths
http://www.audioholics.com/loudspeak...act-or-fiction
Sounds like you are having room acoustic issues and should try moving the speakers around until you find the flattest bass response at the main listening position. You are experiencing bass peaks and dips at different frequencies. You might (probably) need some acoustic treatment in your room.
Cartridge tracking force should be optimized for best tracking, not too little and not too much. If increasing the tracking force improved sound, that's good, but you need to measure to make sure it is not too high.
You need to acoustically isolate the table and cartridge system to avoid room resonances affecting it. The location of the turntable is probably at a room mode where there is a peak in level at the frequency that is causing the problem. Does the table have a cover that can be closed to isolate the cartridge?
You only need more power if the amp clips before you reach the SPL/listening level you want.
Re: bass on records vs CD's: due to the physical limitations of cutting vinyl, records have to roll off deep bass extension and limit the amount of bass. CD's do not have bass limitations.
You should try the amp plugged straight in to the wall to see if it performs better, it might.