If you are having problems dragging, you are not using the proper anchor for the bottom. (Back to my advice to carry several types of anchors, which are suitable for various bottoms). More chain may help--but not solve the problem. Some is also technique of setting. Lower to the bottom, as the boat has stopped. Let the boat slowly drift (or in and out of gear to give slightly sternway) until 3/1 scope has been achieved. Check and see if the anchor is set. Slowing let scope out to 7:1, and apply reverse power, to be sure that the anchor is set. When we were cruising, where we anchored at lest 200 days a year--we would give at least 60% stern power (enough to give 4 knots if we had way on).
As for chocks--if properly installed and backed, and the correct type, OK--but I tend to avoid them in the C Dory or other small boats. I tend to put cleats near the railing, and then put SS rub strips on the glass where the rode or dock lines would pass over the glass. As Tom noted, most of the chocks are not sturdy enough to take a good load, they are screwed in place, and may have sharp edges which can abaide lines. I do not take the full anchoring load on the roller---I like to use a line to the bow eye (shackle), but you can loop around the cleat and on each side of the anchor roller (with the snubber line)--that way you don't chafe the anchor rode.
The chocks I like the best have a SS base, which is bolted thru the deck with a backup plate. They have smooth / rounded sides and a captive pin on the top. These are Panama Canal type acceptable (if you are taking your dory through the Canal....) But probably overkill for the C Dory 22!