You don't really need to use a quota question to solve this problem. You can use a free format hidden question for example. Pop this question on an existing page where all respondents see the page.
This example below randomly creates an integer between 1-10.
<input name="HdNumRand_CODE" type="hidden" value="
Begin Unverified Perl
You can now reference the random number "HdNumRand_CODE" for skip purposes later on in the survey.
Another option, depending on your Sawtooth version is to use the SetValue and GetValue functions.
Just with the quota question approach, I would first make sure I am referencing the correct quota question names and then make sure the quota question is operating correctly. Do some test surveys and check the quota question data. Once you are convinced that is working okay, I would then concentrate on the skips.
Regarding you block questions and skipping within the blocks, look at the pull down menu for "Skip To". You will see all the questions you have defined but up the very top you have ...
<End of Block>
I'm guessing this is what you are looking for to assist your skipping control within the block questions?