Hi mate.
Personally..and it is purely personal..
I'm ugly with a rough Northern accent. I don't scrub up well. Mailshots have proven a reasonable way for me (1 in 50 success rate). This means producing a reasonably professional kit and sending it out. I'm happy to mail you samples of mine.
Visiting personally if you're a charmer is great. Sammie got us 3 shoots in a day. But as you said it's time consuming and soul destroying. Personally I'd drive round and look for vermin activity. If there is none - the farmer isn't going to want you shooting and you don't want a dead piece of land to tie you down anyway. If you see some it's a good in "sorry to bother you but while having sex with your sheep / cow / daughter (delete as appropriate) I saw xxxxxxx munching your crops. I do vermin control...blah blah blah..
Have your insurance and look smart.
Good luck, it's a ****ty job