Can you use "many, many" in this way?

One issue is that you are using many, many to compound the number. It doesn't do that: it simply emphasises many. Where an adjective is simply repeated for emphasis, you can't repeat it in the style of your second sentence.

My love is like a red, red rose
*My love is like a rose which is red, red.

However, it can work if you need it for emphasis in the second form:

My love is like a rose which is red, red!

...but that is quite a particular use.

The phrase lots and lots doesn't work in the same way: it's effectively a single unit, just as red or many is. Because it's a single adjectival phrase and not repeated, you can place it at the end of the sentence.