Has anyone managed to breed them without live food? Would Insecta Pro improve the chances?
Yes. I have bred them previously on sprouted seed mixed with egg&biscuit powder + half-ripe grass seed as the only rearing foods. They will very readily take softfoods. Just mix some softfood powder with some sprouted seed to introduce it. Even pieces of madeira cake (& similar) are keenly taken by RFPFs. Any greens, cucumber, etc. too. They are really not at all fussy eaters & will readily try new foods compared to most other finches.
I agree that they will breed without live food but they eat live food in the wild so if you can provide it they will do better in my opinion. I tend to get more and much bigger, stronger young when they have access to mealworms combined with all the rest that has been mentioned. It's easy to breed your own mealworms and really worth a go.