What I do, hence I think this is the best or efficient way to go, lol, is cut the meat into chunks - of course remove all fat, ligaments, etc aka “silverskin” - and wrap it in shrink wrap tightly getting rid of “all” air, then butcher paper, and freeze it in packages of desired weight (mine range from 0.5 to 1kg and in between). Take out when needed and grind it in semi frozen state if possible or whatever, really. You always have fresh grind that way and best preserved meat because it will always be fresher when frozen in large chunks than “burger”. That way you can also grind it together with pork or whatever you are adding on the spot as you go without a fear of fat spoiling or whatever and it is easier to mix things up when you grind them together. The chunks of meat wrapped properly the way I described above will last a very long time in your freezer and you would always have fresh meat to grind and add whatever you want because you may want to add different proportions of pork, for example, depending on the dish; or bacon; or nothing at all.
For the price of butcher, I bet you can buy a semi-decent grinder that will last a very long time and go through many deer. I used to run a hand grinder doing exactly what I described above. I bought it for… hmm… don’t remember, probably for ten bucks at Homesense or something like that. Worked just fine for a few years. I then looked for a good hand grinder for a long time, but couldn’t find anything and I bought a LEM #8 and I still do it the same way - grind on demand sort of thing. So in hindsight, I’d probably buy something significantly cheaper (though it is a not very expensive grinder).
Also, as far as the vacuum sealer goes. I know it is great and many people do it that way. Personally, I think it is too time consuming and it is much cheaper to buy shrink wrap and butcher paper and it serves the same purpose and the same or close results. Whatever the shrink wrap costs, I don’t remember because I bought a huge roll they sell in grocery stores a couple of years ago and still have it. Butcher paper is $30 per roll in Costco online (cheaper in store); I just ordered and already received my new roll. The previous one lasted probably five years or longer, no idea. And I wrapped some moose, elk, bear, and deer, not sure how many. So that’d be 50 bucks or less worth of packing material. It is also much faster to wrap it this way than vacuum seal it.
I really don’t see the advantage of vacuum seal if you aren't planning on keeping the meat for an unreasonable amount of time. That roll of paper will probably last a couple of decades if not longer wrapping a deer or two per season.
Sorry, no help with the butcher. But, especially if you are deboning the meat anyway, just put a little more work into it and do it yourself if time permits.