Typically when 3003 aluminum is welded to itself 1100 (at least according to D1.2)  I've done plenty of non code work with 4043.

3003 is minimally alloyed and I suspect that the 5000 series fillers have an "over alloying" negative effect of some sort.

According to D1.2 

3003 is an M21 grouping base metal

1100 is an F21 grouping filler metal

5356 is an F22 grouping base metal

4043 is an F23 grouping base metal

At least according to D2 the F groups are an essential variable ( I assume with good reason)

Here is the most complicated filler metal chart I've seen in my life :)
http://www.hobartbrothers.com/downloads/aluminum_filler__eNttQ.pdf

It allows for several fillers for 3003 base metal.. But no 5356

Sorry to be so unhelpful...  I think it may be a "fit for purpose" issue if your doing non-code work..  But I would not move forward (without a competent engineering variance) with an filler that neither the manufacturers or code accepts if it is for anything other than home shelving or decorative work :)