I suppose it's safe to say you've investigated the front derailleur. I know they offer Speeding tikits w/ a Shimano FD2300 Braze Double (or sub 2200). Are they customizing those frames to place the derailleur?
I think Lynette Chiang had the H-bars on her Tikit. It was a size small but seemed to fold as well as any other tikit in her videos.
Re. using the front rack for shopping w/ the Tikit, I think it's fine to do it and is a good little workout, but honestly, putting the folded bike in a shopping cart is probably going to be easier.
Unless you really need the cargo space for a long tour or work, I'd say save the weight and just use your rear rack. If you do get your showercap though then the front rack is helpful for allowing you to wheel the capped bike.
I lived in Salt Lake, so I'm not going to fault you for driving 2 blocks in the winter, but I do hope you can take advantage of your bike in better weather to complete those sorts of errands.