That sounds like a pretty ambitious trip for two days.
I have not specifically done all of what you propose, but have spent a fair bit of time exploring the area generally.
Both Upper Bungonia Creek and Spring Creek (which Dog Den flows in to) are classed as "canyons". Spring Creek requires ropes (I would assume 2x 30m - not 30 foot). Spring Creek is supposedly closed due to loose rock.
http://bushwalkingnsw.com/park.php?nid=32A lot of the Shoalhaven Gorge upstream of Bungonia Creek is very steep sided, but
generally possible to walk up IF you pick a good spur or creek- with a few major exceptions such as Spring Creek/Blockup Gorge area. Many of the smaller side creeks are very pleasant walking generally speaking, and I would think Becks Creek would be a reasonable exit option.
How about heading down the red track through Bungonia Gorge (with a side trip up to Jerrara Falls), down Bungonia Creek to the Shoalhaven then upstream and out Becks Gully. There are some very pleasant campsites on the big beach about 1.5km to the south of Bungonia Creek on the Shoalhaven. It is possible to stay on the W bank (steep and rocky in places) heading south along the Shoalhaven until these campsites. With a side trip/explore of Jerrara Falls this would be at least 3/4 of a day, if not more. You will need to cross over to the base of Fools Gold Gully as you head south, as the west bank will become impassable.
I'd suggest taking a lilo or drybag to cross the river as it is not always straightforward to cross it where you want (big, deep and wide pools that continue for a kilometre at a time). As the current in these pools is often minimal, it is very easy to paddle upstream on the pools. If you haven't been to the area before this would be a very solid introduction to get a feel for what is one offer.
There are lots of other options in the area, many of which can be joined together with liloing sections of the river. The area around Greater Horsehoe Bend is another standout walking spot. A great trip is from Little Horsehoe Bend -Tims Gully - Sparkes Falls - Peach Tree Canal - Wineglass Tor - Poddy Dodger Spur - Greater Horsehoe Bend. This is a solid and spectucalar two day walk (nearly all off track- beautiful open walking country for most of it).
Clarence