I don't really mind SAPR not being an exact replica of their irl counterparts when it comes to their duties. I've had a lot of RP generated as being part of SD just because SAPR stumbled across something patroling the great empty and called for us.
As for the hunting job, maybe the payout or entry cost for the job can be adjusted if it's such a big problem, but SAPR walking up to you mid hunting shouldn't be an issue. If anything it's giving more roleplay to you, eventually your character would be known in the are so you don't have to get bugged for a license everytime. Just like how frequent hunters irl would eventually know their local rangers and what not.