Because of a couple of issues here related to your wife's carpal tunnel thing I'm going to deal with your points in a mixed up way.
- Long / variable reach (this was a 27" wheel bike converted to 700c wheels)
When you swapped over you increased the reach from the pivot to the pads. This increases the force needed to achieve the original stopping force. Most will not notice this issue but because of your wife's CT issue this is just one point that is adding up to the overall problem.
- Most important: the force required to actuate the brakes is less than that required for an 80's vintage Shimano design. Would a dual-pivot design require less force? Center-pull?
A set of longer reach dual pivot Tektro calipers will greatly reduce the lever effort needed compared to what you have now. I've done this swap on two bikes of my own that were originally 27's converted to 700 and the reduction in lever effort just with the caliper swap was amazing.
- Not a recessed bolt mount
Tektro makes a bunch of longer reach calipers that will work but I'm just not sure of which exact model has the long bolt and regular nut style. You may need to email them directly on that aspect to know which to order. The sets you're looking at are the R538, R556, R365,R358 and R316. I know that the 538 and 556 are both the sorter stud tubular nut models. But it's not hard to drill the back of the fork to 5/16 to accept the tubular nut and only slightly more complex to do the rear bridge.
- Clearance for 700C x 28 tires, fenders are optional
Won't be a problem at all with any of the noted models. One of the bikes I converted is running with 28's using the R538 calipers and there's gobs of clearance.
- Compatible with flat-bar levers
This may be your biggest downfall on two counts.
First off most flat bar levers these days are designed to pull a lot of cable to use with linear or V brakes. This is not suitable for any of these sidepull calipers as it again reduces the leverage ratio and will make her have to squeeze that much harder. What you need to find is some old cantilever levers that have the much shorter pivot to cable barrel end distance to raise the leverage ratio. The lever swap combined with the switch to the dual pivot calipers will combine to greatly reduce the pressure she needs to achieve an easy stopping power. A suitable option if you can't find any old cantilever levers is to get some Avid Speedial levers. These have a little adjustable shuttle for the cable that can be dialed in and out. In this case you would dial it so the shuttle goes inwards as far as it can towards the pivot. This would make these levers compatible with the caliper brakes. When dialed out they are then compatible with linear or V brakes.
Second, if you're using mountain bike flat bars on this bike you have to realize that the simple flat design twists the bones in the rider's wrists so the forearm twin bones are all wound around each other. And that takes the carpal tunnels with them. If you can do a handlebar swap to a style like a ^-^ or upside down W shape then the angled grip areas will allow her to ride with her forearm bones in a much more neutral position and the carpal tunnels will similarly lay in a nice path that doesn't make them apply pressure to the forearm bones when flexed for braking efforts. Also by moving her hands back a little with these bars it would also take a little more weight off her wrists which would further reduce the discomfort. Being in Vancouver you're in luck. I recently bought a set of bars with the bend style shown in my little graphic from Sports Junkies down on Broadway just on the east end of the block where MEC is located. The bars were aluminium, cost was about $12 and the size is compatible with mountain bike levers and stems.
On top of this I also highly recomend an immediate swith of the brake pads on whatever brakes you get to the Koolstop salmon colored ones. The initial bite and overall feel of these pads is one that again produces more stopping power for less lever effort.
But the pads alone will not do the trick. The setup you have right now is stacked too much against using any single one correction. If she's having a hard time of it then you need to pretty much redo the brakes AND swap out the handlebars. You basically need to convert the bike to an upright sitting cruiser to take the weight off her wrists and to let her arms form a very neutral and natural reach to the bars and levers. This last bit you'll get from using the ^-^ shaped bars and by setting the angle of the bars in the stem and the levers on the bars so that they are neutral to your wife's reach to them. A good way to set this up is have her sit on the bike and with her eyes closed just naturally lift her arms to where she THINKS the bars and grips are located while not twisting her wrist and hands out of their natural resting position. This last bit may take a few tries if she's not really sure and keeps trying to put her hands into the position she remembers the flat bars forcing on her. Doing all this will cost you on the high side of $100. But the good news is that if the bike otherwise fits her half way decently that you would not require a different bike if she enjoys riding. But keep in mind that the casual upright seating position demanded to take her weight off her wrists is not going to make for a spirited and sporty riding speed. There ARE options for folks that want to ride fast and have CTS but that's a whole other ball of wax. Just now it sounds like you're just looking to make it practical for her to join you on some rides for fun and sightseeing and maybe a few grocery errand rides. For that a nice casual bike that doesn't leave her in pain be fine.