Well, in the first instance I think that the various shooting organisations need to engineer a position of some power, if you have no power or support it is not a position from which you can make demands. I imagine this will be a long road to travel and will require considerable strategic planning. At the present time the general population, which is mostly urban, gets its view of guns from an anti-gun media and so the public view is generally speaking in keeping with this.
As I've indicated earlier I think that licensing conditions and restrictions should be based upon a reasonable application of knowledge and a quantitative approach to risk. I often quote that it costs me £600 to insure my car and only about £10 to insure my shooting and the money rarely lies, if it did the insurance companies would long since have gone bust. The evidence clearly indicates that legal shooting and shooters are not a significant risk to the general public or themselves.
Such an approach would dispose of many of the mad conditions we see today, for example recently someone was allowed to keep a big game rifle but was not allowed to shoot it in the UK. Under my "reasonable and measurable" proposal the police would have to indicate that there was evidence that people with big game rifles intended for use in Africa posed an increased threat to the public if they were allowed to use and zero them here in the UK. This would have to be supported by figures showing incidents where there was a clear threat to the public good. If such a risk could not be demonstrated and supported by evidence then there would be no reasonable excuse for a restrictive condition limiting the gun owner.
In your specific situation the police would have to show that it was reasonable to ask you to apply to be allowed to use your rifle each time you booked some stalking, and that it was reasonable that such a request would take months to process leaving you having to book days months in advance. They would also have to demonstrate that there was a proven increase in the risk to the general public by allowing you to shoot deer with your rifle and, in view of your stated position, I can't see how they could possibly prove that adding deer to your ticket would increase your risk to the public in respect of a rifle you already own and use on a regular basis.
So, I believe making them quantify any risk that a condition was introduced to eliminate plus making them subject, as most of the law is, to having to be reasonable will abolish most of the mad conditions we see. The bottom line is that legal shooters pose virtually zero risk to the general public and so there is no reasonable justification to place restrictions on their actions based on some imagined risk which has no quantative basis. Each year about 141 people die putting on their trousers, I am not aware of the police conditioning trousers even though the risk to the public is much higher than that posed by legally owned firearms.