You have to consider the interior width of the cabinet. With a 24" trash, you're only going to have about 18" between the stiles for a pull out. If the 15" trash that you have is an actual measurement, then you'll only have 3" left over for storage. After the divider is done, even if he only uses 1/2" for the box, you'll only have 2". Enough for a cutting board or a cookie sheet, but that's it.

Use the cabinet company's pull out, and put that 3" into the adjacent cabinet.

As you can see in the picture, my trash pullout is not centered on the attached door. My trash pullout is below my sink in a 39 inch cabinet. The door is 19 inches wide. The bracket for the pullout is attached 1/2 inch from one edge of the door and 4-1/2 inches from the other edge. Since the pullout is part of the sink cabinet, I mounted the pull vertically to match the other cabinet door. So not only is it off center but the pull is vertical and it has been working perfectly for 2 years now.
Hope this info helps with your situation

If you have kids (or a husband, LOL) be prepared for the trash to sometimes end user up not making it in the trash, probably a little more so with the store bought trash holders. I wouldn't want any baking pans or cutting boards in my trash cabinet at all. Maybe you could use the exte space for a box of trash bags and maybe a cleaning bottle?

I considered moving the trash to a different cabinet that is smaller, but I really want to keep it near the sink. (although it is currently located under my cooktop and I actually really like it there!) And I can't deduct 3" from that cabinet and add it to another because of where it's located (between supersusan corner cabinet and sink cabinet) The space will be completely divided by a wood partition from top to bottom, front to back, so I hope that garbage doesn't get in there!! However, I really only wanted to keep serving trays in there, which I don't use all that often and would probably rinse off before use anyway.

Badgergal, that's exactly what I was thinking!! Was it difficult to get the trash hardware placed on the door exactly where it needed to be so that the door would fit into place correctly? That's my concern...especially since the doors are inset. I'll probably leave this for my contractor but I kind of need a plan in place to know if I should order an unattached door for that cabinet (to attach to garbage) or a regular door that opens to the side.

lcskaisgir, my trash pullout was installed by the Amish cabinet maker who made my cabinets. I was home when they did the install and they had no problems getting it in place. My DH and I have very minimal DIY skills so we generally leave anything that involves measuring and/or cutting to the pros. Our GC was a master carpenter so I am sure he would have been able to install it too. If your GC says he can do it then I would let him. If a mistake is made then it would be on him to correct it.
Hope you can get the pullout to work for you

Did you consider a:
-15" waste + 9" tray base
-18" waste + 6" spice or apothecary pullout

I would want the trash pullout done by the factory. Who are you using? Purchase the best that you can. Showplace offers a deluxe, soft close one that is VERY nice.

Another thing to consider is a 24" door is very wide. And a pull out trash front is always the first thing to get off kilter and need adjusting.

I agree that 18" is PLENTY for your trash pull-out (we had double bins in an 18" pull-out in our previous kitchen, and are doing that again in the new one --- the line of cabinets we're getting makes a double bin version in 15" too). We had two narrow cabinets making up the difference --- between the trash cabinet and the cooktop, we had a 9" pullout for condiments which may have been my very favorite thing in the kitchen, and to the right of the cooktop, we had a 6" tray base (or maybe it was 9"). Loved it all.

i put my trash pullout in my sink cabinet. my sink cab has two doors and one door is attached to the trash pullout. the other opens normally. i put the trash pullout off center to maximze space for other items in the sink cab.

DH and I installed it ourselves. it was fairly easy to do and looks similar to badgergals'.
my cabs are frameless though so that might make a difference. getting the right size trash pullout is key to avoid the plumbing, etc.
here is a pic

michoumonster, thank you for sharing since I am still trying to decide where my trash will go. I like this idea in the sink or a smaller cabinet so I will not use up much space.

Lisa, what have your decided to do with your trash? Thank you! I am so excited for you since I think you are installing your cabinets right now. Please do share.

Thank you for the fantastic solution and picture, michoumonster. This is what I am hoping is feasible, so it's great to see it implemented successfully.

michoumonster, thnx for the idea for the temp pulls. I was using blue tape, that breaks every third time I use it. I will use the blue as a base, and HD tape for the temp pulls until they are installed next week.

We are getting close, Thursday and Friday the molding goes up, and door/window trim finished. New gas fireplace will finish it off nicely.