There are some other options you could consider:
1. Look into getting some new 27" wheels with modern hook-bead rims. 27" rims are still made and these will keep your tires from blowing off.
2. Look into converting the bike to some modern 700c wheels.
3. Sell the bike you have and look for a used bike that is less than 25 years old. This will have more modern 700c rims. Oddly, this might even be the cheapest option of the three.

These would all require some money, like maybe $100 - $400.

For tubes, Price Point (pricepoint.com) sells discounted tubes in quantities of 5 and 10, plus they are on sale at times for even better prices.

But, it seems to me that changing the wheels or the bike is a better long-term option. If you are rolling tires off of your rim, you have a safety issue.