Pandas - Copying to Index and Then Sorting - python-3.x

Question

I am working on a large dataset of stock data. I've been able to create a multi-indexed dataframe, but now I can't configure it the way I want it.
Basically, I am trying to make an index called 'DATE' and then sort each smaller set against the index.
Right now it looks like this:
+------------+----------+-------+-------------+-------+
| DATE | AAPL | | GE | |
+------------+----------+-------+-------------+-------+
| DATE | date | close | date | close |
| 05-31-2019 | 05/31/19 | 203 | 04-31-2019 | 9.3 |
| 05-30-2019 | 05/30/19 | 202 | 04-30-2019 | 9.3 |
| 05-29-2019 | 05/29/19 | 4 | 04-29-2019 | 9.6 |
| | | | | |
| ... | | | | |
| | | | | |
| NaN | NaN | NaN | 01/30/1970 | 0.77 |
| NaN | NaN | NaN | 01/29/1970 | 0.78 |
| NaN | NaN | NaN | 01/28/1970 | 0.76 |
+------------+----------+-------+-------------+-------+
Where DATE is the index.
And I want it to look like this:
+------------+----------+-------+----------+-------+
| DATE | AAPL | | GE | |
+------------+----------+-------+----------+-------+
| DATE | date | close | date | close |
| 05-31-2019 | 05/31/19 | 203 | NaN | NaN |
| 05-30-2019 | 05/30/19 | 202 | NaN | NaN |
| 05-29-2019 | 05/29/19 | 4 | NaN | NaN |
| | | | | |
| ... | | | | |
| | | | | |
| 01/30/1970 | NaN | NaN |01/30/1970| 0.77 |
| 01/29/1970 | NaN | NaN |01/29/1970| 0.78 |
| 01/28/1970 | NaN | NaN |01/28/1970| 0.76 |
+------------+----------+-------+----------+-------+
Where the index (DATE) has taken all of the unique values, and then all of the rows within stock symbols have moved to match the index where 'date' = 'DATE'.
I've tried so many attempts at this, but no matter what I can't figure out either one. I can't figure out how to make the Index a list of all of the unique 'date' values. And I can't figure out how to reformat the symbol data to match the new index.
A lot of my troubles (I suspect) have to do with the fact that I am using a multi-index for this, which makes everything more difficult as Pandas needs to know what level to be using.
I made the initial Index using this code:
df['DATE','DATE'] = df.xs(('AAPL', 'date'), level=('symbol', 'numbers'), axis=1)
df.set_index('DATE', inplace=True)
I tried to make one that kept adding unique values to the column, like this:
for f in filename_wo_ext:
data = df.xs([f, 'date'], level=['symbol', 'numbers'], axis=1)
df.append(data, ignore_index=True)
df['DATE','DATE'] = data
pd.concat([pd.DataFrame([df], columns=['DATE']) for f in filename_wo_ext], ignore_index=True)
But that didn't cycle and append in the for loop that I wanted it to, it just made a column based on the last symbol.
Then in terms of sorting the symbol frame to match the index, I still haven't been able to figure that out.
Thank you so much!