DNG is a RAW format. There isn't just one RAW format, there are several. Every camera maker has one, and Adobe's DNG creates a RAW format that wouldn't disappear with a generation of camera models.
Not sure about your process creating a web gallery.
But here's a step by step guide on how it works flawlessly. There is not difference if the selected files are DNG or any proprietary RAW format, TIFF, PSD, etc.
1. Create a collection, name it e.g. "landscape gallery"
2. Drag all the images into the collection. The originals stay in their original location, but virtual copies will show up in the collection.
3. Once you have all the images in your collection, click the web module.
4. In the web module you decide which mode to use to display the photos. I, for example, use the airtight viewer, and so I click on the airtight viewer.
This shows all the selected images in the airtight viewer. There are controls to the right, where you can adjust image size and quality. Lightroom automatically creates JPEGs out of the images in the selection.
Some of my files, coming from Photoshop, are quite large, but the conversion is quick.
Key is, that you don't have to reformat any photo. Changing to the web module does this automatically, and quickly. No way it takes a minute per photo.
Hope this helps.