I'd like one of the Dickey's work shirts with a big CARBOY logo on the back in addition to the embroidered one on the chest
Not sure that's an option. Here are some snippets from their printing FAQ page:
Q. Can my logo be printed in two locations?
A. Yes, you can choose to have your logo printed in two locations such as left chest and full back for an additional fee. For all digitally printed items the second logo location will add $2.50 per item. However, screen printed items the second logo location price will be based on the number of items ordered and is included with the pricing information on each style page.
Q. Can I order embroidered shirts and printed shirts on the same order?
A. Not at this time. However, you can of course place separate orders for embroidered shirts and printed shirts.
Q. Why can't I order the same items for digital print that I can for embroidery?
A. Digital printing is a very specific process which requires apparel especially designed for direct to garment printing. While embroidery can be done on a large variety of materials, digital print can only be done on cotton fabrics. Some of our most popular items for embroidery will not work for digital printing due to the fabric content, texture and ornamentation such as buttons or zippers. You will find our complete line of items available for digital printing under our Printed Apparel categories.
http://queensboro.qbstores.com/about-printed-apparel.htmlEDIT: plus I don't see the Dickies shirts listed under digitally printed items:
http://queensboro.qbstores.com/printed_all/all-products.html?spp=61Kevin