Here's a pretty complete definition of conquer. I don't think that it quite fits your definition of the word. Regardless, if "conquer" offends your sensibilities, I will try to avoid its use.

The last word is yours, if you want it.

1 : to gain or acquire by force of arms : SUBJUGATE
2 : to overcome by force of arms : VANQUISH
3 : to gain mastery over or win by overcoming obstacles or opposition <conquered the mountain>
4 : to overcome by mental or moral power : SURMOUNT <conquered her fear>
intransitive senses : to be victorious
- con·quer·or /-k&r-&r/ noun
synonyms CONQUER, VANQUISH, DEFEAT, SUBDUE, REDUCE, OVERCOME, OVERTHROW mean to get the better of by force or strategy. CONQUER implies gaining mastery of <Caesar conquered Gaul>. VANQUISH implies a complete overpowering <vanquished the enemy and ended the war>. DEFEAT does not imply the finality or completeness of VANQUISH which it otherwise equals <the Confederates defeated the Union forces at Manassas>. SUBDUE implies a defeating and suppression <subdued the native tribes after years of fighting>. REDUCE implies a forcing to capitulate or surrender <the city was reduced after a month-long siege>. OVERCOME suggests getting the better of with difficulty or after hard struggle <overcame a host of bureaucratic roadblocks>. OVERTHROW stresses the bringing down or destruction of existing power <violently overthrew the old regime>.