I decided to really slow myself down. I ended up using

one sheet of paper for two days:
I tried tracing the bear head to get a better feel for what I was trying to copy. I then drew some extension lines to guide my free hand drawing. (Fellow-blogger, klangley, suggested a similar approach. Just goes to show you that great minds (and otherwise) think alike!
I then moved on to the oval-based cartoon characters in the middle of the page. I drew six ovals in a row and then filled in the details. I should have spaced them out better, though, as the bulldog and elephant were kinda cramped. The hats were problematic for me, but I was amazed that I handled the elephant's trunk as well as I did.
Saturday, I decided to try to tackle those
@#%! ears again. I still don't have a really good feel for them, but practice makes adequate (I hope!) On to Sunday...

Since the bulldog head got so squeezed on Saturday, I decided to give him more room on my next pass. I traced the head and broke it down into their components and then took a pass at it, on a larger scale than I had been working. (What's that black area around his eyes supposed to represent? Reminds me of Mack Swain!)

A minor epiphany: I was throwing everything off by drawing the eyes too big for the head! On my second pass I deliberately drew them smaller and it really helped.
I sketched out a few basic ovals doing this and then noticed I was speeding up and becoming really sloppy again! The
tilt of the eyes suffered as well. I drew another "Barney" using the smaller eyes approach and liked how the face became more fleshy. Not on model by a long shot, though!
There's still lots of work to do, but after only a week, I am noticing progress of a sort...