The OPs apparent issue with with taking hands off bars to shift.

OP, personally I would try a set of Suntour indexed 7 speed bar ends first. They come up on eBay and do go for a little $$$ but if you don't like the barends you'd scarcely lose any money on them. The resale will be whatever you paid probably. That would give you another shifting system to try without going the Full Monty drivetrain transplant.

If the barends don't suit you, sell them, then look at Shimano/STI/brifter options. And, if you do go this route then personally I'd look at 8-speed...more options in brifters and such when you get to 8-speed. It would require a hub transplant on your rear wheel (woudn't recommend an 8-speed freewheel) but in the grand scheme of things the cost of the hub swap may be made up for by more available and possibly cheaper brifter options.

Good luck!