Ditch the inserts for your trip. At least ditch the front one. But really just ditch them both.
Logic I used for Italy trip was that I wanted to be able to change a flat on trail. Cushcore is great for our local trails when we can ride it out to the car. But in Italy, an unchangeable CushCore flat could have us hiking back up several hundred meters and many miles before the end of a ride. Plus, some of the trails end with 4-5 miles of bikepath to town, which would be unpossible on a flat Cushcore. Get over it and budget for the occasional flat with innertube repair like we did in the olden days.
Edit: Found this how-to for building a DIY corrugated plastic bike box: https://www.endlessmountainsar.com/n...ook-bike-boxes Based on quick googling, the plastic is maybe 0.15 lbs/sq ft. For 2 sheets, that would be about 10lbs. With whatever straps, rivits, buckles, etc are added to make it wour, it'll probably end up being close to a proper bike bag.