Dynamic named range using a range within a range

[Nox000]

I have the following worksheet:

       A         B         C         D          E
      +-----+-----------+---------+--------+-------------+
    1 |FALSE|Lot ABC123 |Product 1|Used qty|remaining qty|
      +-----+-----------+---------+--------+-------------+
    2 |TRUE |Lot ABC321 |Product 2|Used qty|remaining qty|
      +-----+-----------+---------+--------+-------------+
    3 |TRUE |Lot ABC456 |Product 1|Used qty|remaining qty|
      +-----+-----------+---------+--------+-------------+
    4 |FALSE|Lot ABC111 |Product 3|Used qty|remaining qty|
      +-----+-----------+---------+--------+-------------+
    5 |     |           |         |        |             |
      +-----+-----------+---------+--------+-------------+
    6 |     |           |         |        |             |
      +-----+-----------+---------+--------+-------------+

with the purpose to create a drop-down list in another worksheet, I've created a dynamic named range for the column C that picks all cells up to the last used one with

=OFFSET($C$1,0,0,COUNTA($C:$C)-0,1)

Now, Is it possible to create the same range but only with the products that are still available (E>0) ?
Tried with

=IF($E1>0,OFFSET($C$1,0,0,COUNTA($C:$C)-0,1),"")

but ofc it didn't work.

Since the values selected from the drop-down list are used in a different worksheet to fetch values found in column B of this worksheet, a further step would be to tell excel that once "E1=0" it should interpret any new "product1" as the product1 in C3 instead of C1, and fetch B3 instead of B1
I guess this last step will require a bit of VBA...

Any help would be appreciated!
Thanks!