coupled oscillators (maybe 2/3rds of the code here was copy and pasted from previous things I wrote)
monte carlo estimate
If you need another feature, you can just write a reusable object once, and copy and paste it next time you need it.
One place you might suffer is with inserting LaTeX equations. This could be overcome, probably still in jsfiddle, by importing MathJax, and using an html div element with absolute positioning, to position it over your graphic. Another place might be loading a local image file (khan academy, at least, has blocks to try to prevent you from doing this)
I've also heard good things about Sage, despite never having tried it, and I know there's an online in-browser application.
As a case example, since time is a serious concern for this, I did the squiggle drawing thing you mentioned. Khan Academy applet here. From time of opening the tab to completing the code (and fiddling around with the values) was 7 minutes (w/ gracious overestimating of time). Try scrolling to the bottom and messing with the color/size/position options, using the color chooser and built in IDE draggable bars. And keep in mind for future squiggle lines you can copy and paste the function.