That is one solution to a problem we all have, whether we know it or not. Thank you for the idea.
In my case, I came across a bidet at Lowes that consisted of a hand sprayer & fittings. Being tired of the two-liter-coke-bottle full of water used to rinse the back side of the toilet after use to prevent untoward odors, I bought and installed said sprayer on the back of my toilet. Now I have the best of both worlds: a bidet for rinsing off my bum after conducting business AND a sprayer to rinse the back side of the toilet bowl AND an easy way to add those extra gallons the OP mentions.