Hunt for whatever is causing the leaks. It is possible you have a bad seam, but It may be something else too.

Mark the valve on the old tire. Find the hole in the tube. Look at the tire and rim for a possible cause. Those radial tire wires are often almost invisible. There have also been suggestions of using cotton balls (never tried this myself). Pick out any glass from in the tire treads.

Googling "27 Thornpproof tubes", I came up with a few Kendas which would be worth considering.

https://www.biketiresdirect.com/prod...inch-road-tube
Kenda Thornproof Tube - Outside Outfitters

You can also patch your old tubes. I used to shave the seams down with a straight edge razorblade, but sanding seems to work well enough.