Happen to have overheard this conversation. Have been eavesdropping around the Nu quarters 
I thought it to be nice to post a bit of teaser in preparation to get some support for some further work on the NuDroid App. This instead of starting with a large complex proposal.
Let’s look at this bit a bit further as we have at least two potential supporters!
Opportunity
One of the most annoying things is waiting for the NuDroid App to synchronise while you are trying to make a payment. To make NuDroid useful for regular use I believe we need to address this problem rather sooner than later to ensure further uptake of the wallet and with that the actual usage of NuBits by end-users.
Potential direction:
The downloading of the current headers in NuDroid have little to no point as they are currently not involved in validation. Leaving them out would speed the initial synchronisation up, especially advantageous for new users, which might get discouraged after a long wait. With this feature NuDroid could also provide an alternative for the PC client for using NuBits. The latest client has unfortunately a very slow synchronisation process which is required to run when starting the wallet for those not running the client 24/7.