Hi Tremens.
The elastic idea you suggest isn't going to help much, you really need to get to grips with the mali weave.
Firstly, is there spare rope on your drum? Is there an end of rope that would allow you to start weaving.
If you don't have any rope left, you can tie another piece of rope onto the drum.
I believe your trouble relates to starting a new row of the mali weave. When you do the Mali weave, you do it all the way around the drum in a straight line and when you meet where you started you start another line.
This may seem a little tricky at first but is not difficult. Check this document under "The Mali Weave", this will explain how to start a new row.
I hope this helps, I may take some photos in the future when I have time...
James
