Derek
No question, if you have your trigger tuned, you should see some improvement, assuming you do your part. 3-4 lbs is perfect for hunting, a target only rifle could be lower but for hunting you have to consider gloves, cold hands, buck fever etc..
Not sure if you are attempting this yourself, but it sounds like you're new to the life so i would recommend seeking a prof gunsmith. A basic trigger job on a remi shouldn't be too much$$. Just a guess but somewhere in the $100-$150 range. there are also after market drop in triggers available. check with Western Gun Parts in Edmonton.
http://www.westerngunparts.com
Hope this helps,