Here's a quick and dirty implementation: http://nilock.github.io/MathSnips/MultQuiz/MultQuiz.html
This was a bit of a seat-of-pants stream-of-consciousness hack job, so the flexibility of the platform going forward is not great.
Usage should be mostly self-explanatory, but I'll mention that the system is biased against questions involving 0 and 1 (eg, it will produce fewer such questions on average) so I suggest including them in your prescribed quizzes. The 'link' updates itself as you change the configuration values. You can configure a quiz with, say, 5 questions and multiplicands between 2 and 7, and load this quiz directly with the link http://nilock.github.io/MathSnips/MultQuiz/MultQuiz.html?numQ=5&min=2&max=7&maxmin=10. This link, in turn, can be fed into a url shortening service such as tinyurl.com in order to produce a url that can be more easily communicated / manually typed. For example, the above configuration has been fed into tinyurl which produced the link tinyurl.com/m8esp94.
Further extension of this particular page will be limited, but I'm happy to keep the current implementation in working order. Where defects are found on this page, the best option is to post them to https://github.com/NiloCK/MathSnips/issues with the New Issue button in the upper right. Posts there will land in my inbox, which is more reliably read than a Stack Exchange push notification.
I have ideas toward a similar but more generalized and robust system, but that's a long term project. I'll post it here should I ever get it off the ground.