I dont know where you hunt. But, you may want to consider that some states (like PA) dont allow SA for hunting. I shoot a Remy 7600 and I have never had a issue with follow up shots. Actually I only needed a follow up 1 time. 30-06 drops them in the tracks if you hit them right. For that matter so does a 30-30, 243, 270, etc...
You can find a gently used 7600 for $300 or the SA version 750 in your range.
Concentrated power is not rendered harmless by the good intentions of those who create it.