I wouldn't recomend the cheapie Walmart or other big box store 27 inch tires. Sure they are thick and wear like iron but they'll make it feel like you're dragging an anchor behind you. However Continetal and a few of the other makers still have some good performing (low rolling resistance) options in their lineups. Included are some 1 inch wide offerings.

However you're right about there being a much better list of options if you can switch to 700c. But from what I can see your rear caliper MIGHT reach, but I doubt it. And the front looks like it's pretty well at the limit for reach already. More importantly though even if they do reach the extra distance will alter the leverage ratios to where you require a much firmer pull on the lever to achieve the same stopping rate. And knowing how poor most single pivot calipers are already I'm sure you'll agree this isn't going to help at all.

EDIT- I just saw you're new post with the closeups of the brake calipers. It sure looks like the pads will reach but do consider the increase in brake lever pull needed to achieve the same stopping power. And, if like I did, you find that these single pivot calipers are a bit weak in performance now you'll hate them when you mount some 700c wheels due to the longer reach.

All is not lost though. Tektro makes two models of long reach calipers that use the dual pivot design. They are the models 536 adn 556. I've been using a set of each on two older frames that were originally set up for 27 inch that I altered to 700c. I rode them both with single pivot long reach calipers and always wanted a more sensitive braking but had to live with it. The Tektros completely transformed the braking on both bikes from a three finger white knuckle experience to a one or two finger moderate pull. I can't say enough good things about them. For your needs I'd suggest the 536. Depending on the reach of the frame and the rims used you may need to file out just a hair of metal at the very end of the pad mount slot. I know I did on the front but not on the rear. Alternately I found that on the 556 with the longer range of reach the pads mounted up near the tops of the slots with no filing needed.

And yes, these new calipers will work with the old levers so you can keep the flying cable vintage look while running with the newer 700c wheels and tires.