Oops, no, rocks and gravel at the bottom aren't the solution and can make water retention worse. Buy a bag of cactus soil and mix in about 25% volume of perlite or pumice or chicken grit. Okay to mix in gravel, just don't layer it at the bottom. Pots of course should have drainage holes (I think you knew that).
Looking at your upcoming temperatures, you should be okay to transplant, but afterwards keep the plants in partial shade (during afternoons, or place in dappled sun under a tree) until they've established their roots and you can see new growth. No full all-day sun, plus keep them well watered during that time. You want to gently knock off the existing soil being careful not to damage the roots. B
Good luck with your plants!