Eliminate the dish washer. Incineration will solve that riddle. Break the glass with pliars, to avoid screwing around with screws.
If it helps you any, I ran literally tens of thousands of eye glass frames. Steve uses a different procedure than I did, but I'm sure we each achieved the same results.
Please let me give you one caution. Some of the eye glass frames are difficult to dissolve in nitric, but they will dissolve. The caution comes from the fact that once the copper based alloys are eliminated, the remaining material creates a huge volume of foam. If you process by heating, it's not unheard of for a 4000 ml beaker to overflow when you have as little as 500 ml of solution and metal present. Keep a container of water at the ready, so you can dilute and cool the container. Otherwise, you will overflow the vessel. It happens almost instantly.
The best advice I can offer you is to do a lot of testing at the outset, so you become familiar with which parts of eyeglass frames do not contain values. I found it was faster and easier to clip them than to process them with acid. Once you know what to save, it goes very quickly.
Old wire frames can be totally processed. Later frames varied. Generally, the side frames that were covered in plastic contained no gold. Nor did the hinges. The ear piece that was flexible, but plastic covered, was generally gold filled. As I said, there are so many variables that at first you will be unsure of what to process. Eventually everything will be familiar to you and you'll know exactly what to discard, and what to save.
I used to incinerate my frames directly in a small furnace I had built (after removing the glass, and clipping the base metals). I dropped them in the furnace, where the plastic was immediately burned. The furnace was hot enough to melt solder joints, so all of the components were liberated. The material was then very easy to handle.
One tip that will serve you very well here. The results of the nitric dissolution will yield some finely divided gold, often even colloidal. There will also be traces of substances (likely tin and lead) that complicate filtration of your gold chloride solution. You can eliminate all of the problems here by allowing the nitric solution to settle well after being diluted. Siphon off the solution, insuring that you do not transfer any of the solids. Check for silver with a drop of HCl or a little table salt. Recover any silver as chloride.
When you have totally dissolved the material, and have eliminated the nitric solution, rinse the mud well, siphon after it settles, then get all of the solids in a filter. When the solution is gone, and this step is very important, incinerate the solids, then screen. I used to pick out the screws, which, by now, had been stripped of any plated gold. I then boiled the solids in HCl, which will remove a great deal of the substances that make filtration of the gold chloride difficult. Rinse, then dissolve the values. Expect that you will have a considerable amount of flocculence in with the gold, which will now be broken down to quite small particles.
I developed this system over the span of a few years, after struggling with the material.
Do not eliminate incineration. Eyeglass frames tend to be very dirty with oils, which give problems in the operation by causing values to float, or to cling to the sides of your vessels.
Hope some of this helps.
It is safe to say, from the first 80 ounces of gold I accumulated, 60 ounces came from eye glass frames. They were once a wonderful source of gold for me. That slowly came to an end.
Harold