Synthesis of 2,3-dihydrobenzo[b][1,4]dioxin-2-yl)(piperazin-1-yl)methanone

My interest regarding Doxazosin made me curious, what's an easy way to synthesis Doxazosin. The first part is 2-chloro-6,7-dimethoxyquinazolin-4-amine. However, I would like to find a simple synthesis 2,3-dihydrobenzo[b][1,4]dioxin-2-yl)(piperazin-1-yl)methanone in order to get Doxazosin. I tried to form a synthesis, however it looks not very effective (too many steps, etc.). 


My questions:


Is there an easier method?


Are there critical errors in my synthesis? 


[![enter image description here](https://i.stack.imgur.com/5CVcx.png)](https://i.stack.imgur.com/5CVcx.png)


1. methyl acrylate bromation
2. formation the 1,4-dioxane via pyrocatechol
3. cleavage of the methyl group with LiOH
4. forming an acetylchloride
5. piperidine


I edited/ improved the steps with the help of Zhe.


