They were no easy to put on 1985 Craigslist bike bought for Ragbrai did not want to bounce my carbon frame for 4000 miles. Nishiki Tri A bike was barely ridden

The rim is a 700 x 25

Tires 700 x 23

Front and back it happened when riding and this time just after I pumped them with the new tires

Assuming they do not have a hook bead what are my options other than new rims would simply putting less air in work?

I have a front spare front rim all my rears are for 10 gear and this much narrower at 6 gear

Thank you all for your answers