Thank you all for such marvellous advice. In particular, I'd like to thank Richard H for the very simple, obvious solution which works a treat:

Allow two connections per share.
Map the H: drive as normal, logoff if mapping fails.
Connect to the share via UNC, logoff if fails.

I just by-and-large added :
Use \\server\%username%$ to my kix scripts along with other modifications suggested and all works fine.

Appreciate the valuable assistance.