So your one advantage is that it looks like your boat is not an inboard. Looks like the 22ft teal's were only made with I/O's or outboards. A stuck inboard can't easily be dragged/rolled/slid out (see above, helicopter!)
Post some pics if you have them! I'd say an afternoon with a couple of guys, some shovels, some block and tackle gear/come-alongs, and some long (6 foot) screw in anchors. (and appropriate beverages and pizza) (also, might not be able to find a screw in anchor that long, but any welding shop can slice and extend a shorter one in about 2 minutes.)
I have personally slid boats that size and larger off sand using 3 screw in anchors, block and tackle, and a come along. I set 2 of the anchors out in the water 10 feet or so (shallow) and hooked the stationary block to a rope bridle going to both anchors. The traveler end of the rigging goes to the boat, and the third screw in anchor is off to the side a little bit to anchor the come-along, which pulls the free side rope on the rigging.