Get any cabinet you like in 18" and find a 16" trash/recycle system from a third party and all you have to do is put that kit in which is only a few screws.

If you want a door mounting kit which you pull out the whole trash kit by pulling on the door, most known manufacturers like the ones you listed who make custom sized cabinets they consider this as AD (Altered Depth) cabinet and you will pay allot of money, because standard size for base cabinets is 24" deep.

Visit this page and I'm sure you can find something here which is not that expensive

http://www.kitchenshelves.com/index.htm

Thank you! My husband I are thinking we will go with the more mid-priced cabinets and go with the third party trash/recycling pull out (his preference) or we could go with an upscale free-standing trash/recycling unit like the one from Simple Human (my preference because a) it's foot operated and b) I can move it around the kitchen based on need --next to the sink during food prep or doing dishes, next to the table when clearing a mess, etc.).

If we go with the third party add-on, I'm assuming we'd order normal cabinet units in the dimensions we want (doors on hinges, one shelf inside, perhaps a drawer above the door?) and then we just take the door off the hinges and attach the pull-out mechanism to the cabinets and door?

Dynasty is a quality mid range line that gives you the opportunity to get an insert customized to your specs. Why wouldn't you go with them? Trying to hack something after the fact that really isn't hackable unless you've got the tools and a good deal of knowhow will only be frustrating to you. If you could do that job, you wouldn't have considered going with someone who could do it for you in the first place. You'd have already done enough cabinet and drawer glide mldifications that you wouldn't have anyquestions about it.

I guess in our budget, Dynasty Omega is top line and Schrock is mid. The quote we got to do the kitchen we want in Dynasty was $17K. The quote we want to do the same cabinet layout/sizes in Schrock was $13K. The only difference was that with Schrock we couldn't get the trash/recycling pullouts where we wanted them (in a section of 18" deep cabinets). $4K seems like an awful lot to pay just for trash/recycling. If I go with the third party "hack" it will cost about $300. We are quite handy and can certainly install the pull out mechanisms. I'm sure thousands of people have had much success adding these units to existing cabinets which is why there is a market for them. Obviously if we had an unlimited budget, I'd go with the Dynasty cabinets, but given budget restrictions, we have to prioritize. As far as asking questions about this situation... isn't that what the Houzz Advice section is for? How would anybody know how to do anything if they didn't ask questions about it first?

You could also just set the trash can in the cabinet. I don't really understand trash pull outs, I guess.

Ha! Good point, emilyam819. :) That's definitely the least expensive, simplest option. Quite possibly we will start from there and see if we even want to bother upgrading.