Is it possible to use 过 with specific time words?
Yes,两个都可以。比如:去了北京与去过北京大体意思是一致的。但是，“去了北京”有已经回来与没有回来两种可能，而去过北京则结果只有一个，那就是现在已经不在北京了！谨记：过的语句后可以加了字，反之不可以！!

Edit (Translation):
Yes, both are possible. For example, 去了 Beijing and 去过 have roughly the same meaning. But, 去了 Beijing has two possible meanings; went and already came back, or went and still hasn't returned. However, 去过  Beijing only has one, you have been but you are no longer there! Remember: You can put 过  at the end of a sentence but the reverse is not true!

(Comment by editor) Im not sure if the last sentence is translated correctly or maybe the OP meant something else. Possibly you can put 了 at the end but not 过。